with talks ranging from
REAL FUNCTIONS and TOPOLOGY via SET THEORY and LOGIC to ITERATED FUNCTION SYSTEMS and FRACTALS with NUMBER THEORY around
Time and place: usually Tuesdays at 10:15 in room A113
in the building of Faculty of Mathematics, Physics and Informatics
of the University of Gdańsk (see at Google Maps)
xor
online.
In case of any questions, please contact rafal.filipow@ug.edu.pl
2026-06-30 - Marcin Sabok (McGill University):
Sums, products, and exponents in two-colorings of the naturals
I will discuss a recent result saying that that for any coloring of the naturals using two colors there are
monochromatic sets of the form {x,y,xy,x+iy:i≤k} and {x,y,x^y,xy^i:i≤k} for any k.
Based on joint work with M. Bowen and R. Alweiss.
2026-06-30 - Nina Snigireva (University of Galway):
Does an iterated function system need to be contractive to admit an attractor?
We will begin by briefly reviewing classical contractive/weakly contractive iterated function systems (IFSs).
It is well known that a contractive IFS admits a unique attractor.
We will consider noncontractive IFSs and investigate techniques which prove useful in studying such systems.
In particular, we will discuss whether an IFS needs to be contractive to admit an attractor.
This is joint work with K. Lesniak, F. Strobin and A. Vince
2026-06-30 - Krzysztof Leśniak (Nicolaus Copernicus University in Toruń):
On the notion of attractor for IFSs
We are going to discuss various concepts of attractors for iterated function systems (IFS):
Hutchinson attractor, strict attractor, pointwise attractor, semiattractor.
Our prime objective is to underline the differences between those concepts.
We illustrate our discussion with several examples and ask some open questions.
2026-06-30 - Tomasz Żuchowski (Wrocław University):
On cardinal invariants related to Rosenthal families and large-scale topology
Given a function f∈ωω, a set A ∈[ω]ω is free
for f if f[A]∩A is finite. For a class of functions Γ⊂ω,
we define rosΓ as the smallest size of
a family $\mathcal{A}\subseteq[\omega]^\omega$ such that for every $f\in\Gamma$
there is a set $A \in \mathcal{A}$ which is free for $f$, and $\Delta_\Gamma$
as the smallest size of a family $\mathcal{F}\subseteq\Gamma$ such that for
every $A\in[\omega]^\omega$ there is $f\in\mathcal{F}$ such that $A$ is not free for $f$.
We compare several versions of these cardinal invariants with some of the
classical cardinal characteristics of the continuum. Using these notions, we partially
answer some questions of the other author and Koszmider and of Banakh and Protasov.
This is joint work with Arturo Martinez-Celis.
2026-06-23 - Anna Wąsik:
An abstract non-piecewise syndetic ideal
2026-06-16 - Krzysztof Caban:
Rate of convergence in the disjunctive chaos game algorithm
[Abstract]
2026-06-09 - Arijeet Mishra:
Full normalization of mouse pair
In this talk, I will present a proof of full normalization of mouse pair that omits extender from the alternate branches.
2026-06-02 - Anna Wąsik: An abstract non-piecewise syndetic ideal
2026-05-26 - Daria Perkowska (Wrocław University of Science and Technology): Operation* in the Baire space
I will present several σ-ideals related to different notions of small sets on Zω, such as
M-, SMZ+, ED, IE, H, and G.
I will show that M- preserves all classical cardinal invariants of the meager ideal.
Additionally, I will present relationships between these ideals according to operation *:
ED* = IE, IE* = ED, H* = G, SMZ+= M-*.
2026-05-12 - Paolo Leonetti (Università degli Studi dell'Insubria):
Ideal core of real sequences and linear transformations
[Abstract]
2026-05-05 -
Wojciech Wołoszyn (University of Oxford):
Modal linear order theory
I will discuss the modal logics that arise from moving among linear orders by embeddings,
monotone maps, condensations, or end-extensions. The answer depends sharply on both the
choice of morphism and on whether one works sententially or allows parameters.
I will explain modality-elimination results for embeddings and monotone maps,
and then describe several exact classifications, including the logics realized by finite and
infinite worlds under embeddings, by Q under condensations, and by finite worlds under end-extensions.
The talk illustrates how simple order-theoretic features already produce a surprisingly rich modal picture.
2026-04-14 - Klaudiusz Czudek (Gdańsk University of Technology):
On a certain characterization of Birkhoff billiards inside discs
I am going to discuss a certain characterization of Birkhoff Billiards inside discs which is related to the expansion of the formal Lazutkin conjugacy at the boundary. The problem is related to the famous question posed by Kac if one can hear the shape of the drum. This is a joint work with Jacopo De Simoi, Andrew Gad and Marco Poon.
2026-03-31 - Anna Wąsik: An abstract non-piecewise syndetic ideal
2026-03-24 - Grzegorz Guzik (AGH University of Krakow): Evolution systems of measures for some discrete stochastic processes nonhomogenous in time
[Abstract]
2026-03-17 - Adam Kwela:
Some corollaries without proofs
2026-03-10 - Jacek Tryba:
Homogeneity of the Folkman ideal
2026-03-03 - Szymon Głąb (Łódź University of Technology):
Non-universal graphs with NNc property
In 2001, A. Bonato posed the following problem: suppose that a graph G has the NNc property, defined by the condition that the
subgraphs induced by the neighbourhood and by the non-neighbourhood of each vertex of G are
isomorphic to G. It is clear that the random graph R has this property, but it is the only known example of such a graph.
Which other graphs, if any, have this property? In his paper On graphs isomorphic to their neighbour and non-neighbour sets
(European J. Combin. 31 (2010), no. 5, 1419–1428), Gordinowicz answered Bonato’s question in the negative.
He constructed a graph with the NNc property that is not isomorphic to R.
However, his graph contains an induced subgraph isomorphic to R. This led Gordinowicz to pose the following question:
determine whether every graph with the NNc property is universal, that is, whether it contains an induced
subgraph isomorphic to the Rado graph. We answer Gordinowicz’s question in the negative by constructing
a non-universal NNc graph. Our construction utilizes the categorical Fraisse theory developed by Kubiś.
Classical Fraisse theory cannot be applied here, since there is no ultrahomogeneous undirected graph
that is a non-universal NNc graph.
This is a joint work with J. Swaczyna and A. Widz
2026-02-17 - Takehiko Gappo (TU Wien): ω-versions of cardinal invariants of ideals on countable sets
In this talk, we study the values of add*ω(I), non*ω(I) and cof*ω(I)
for various (Borel non-P) ideals on countable sets. These cardinal invariants can be viewed
as "ω-versions" of classical cardinal invariants and were previously studied by
Filipów and Kwela "Spaces not distinguishing ideal pointwise and sigma-uniform convergence"
and by Cieślak and Martínez-Celis "On ideals related to Laver and Miller trees."
We present new results and their applications from joint work of the speaker with Cieślak, Martínez-Celis,
and Yamazoe. Our preprint is available on arXiv.
2026-01-27 - Paweł Klinga:
On metrics inducing the Furstenberg topology
We discuss Dirmeier's examples of metrics inducing the Furstenberg topology
and directly prove that a resulting metric space is not complete.
2026-01-20 -
Małgorzata Kowalczuk:
Infima of critical ideals for countable compact spaces
2025
2025-12-16 -
Adam Kwela:
Ideal version of Mazurkiewicz theorem
I will present some partial results concerning Farah's conjecture that every Fσδ ideal is of some special form.
2025-12-02 -
Adam Kwela:
Farah ideals
I will present some partial results concerning Farah's conjecture that every Fσδ ideal is of some special form.
2025-11-25 -
Adam Kwela:
Farah ideals
I will present some partial results concerning Farah's conjecture that every Fσδ ideal is of some special form.
2025-11-04 - Filip Strobin:
On equicontinuity of the Hutchinson operator
Let F={f1,...,fk} be an iterated function system on a metric
space X (i.e. fi:X → X are continuous).
Its Hutchinson operator is the map HF:K(X)→ K(X)
defined by
HF(K)=f1(K)∪...∪fk(K),
where K(X):={D⊂ X:D is nonempty and compact}.
An attractor of F is a (necessarily unique) set A∈K(X) so that
(i) A=F(A)=f1(A)∪...∪ fk(A);
(ii) for every K∈K(X), the sequence of iterations
HF(n)(K) converges to A w.r.t.
the Hausdorff metric on K(X).
It is well known that IFSs consisting of Banach contractions on complete metric spaces
generates attractors, yet there are examples of noncontractive IFSs with attractors.
During my talk I will show that if an IFS F on a compact metric space X admits
the attractor, then the family of iterations {HF(n):n∈N}
of the Hutchinson operator is equicontinuous. This result extends some earlier obtained
ones in which additional assumptions have been made. I will also provide several examples
that illustrate the result and its optimality; for example, I will show an IFS F with
attractor, for which the family of all compositions of its maps is not equicontinuous, and
an example of a single map f on a unit circle with contractive fixed point,
so that the family {f(n):n∈N} is not equiconatinuous.
This is joint work with Piotr Szuca.
2025-10-28 - Aleksander Cieślak (Wrocław University of Science and Technology):
Combinatorics of additive classes
Let J be a σ-ideal on the real line.
We say that a set of reals X is J-additive if X+F is in J for
every F∈J. We will investigate combinatorics of null-
and meager-additive sets as well as strongly null and strongly
meager sets. We will try to include in this discussion
the σ-ideal generated by closed sets of measure zero.
We will show several consistency results regarding variants of
Borel conjecture for these classes and then investigate their uniformity numbers.
2025-10-27 - Maciej Gnatowski (Białystok University of Technology):
Równania diofantyczne z silnią
2025-10-21 - Boban Velickovic (Paris Diderot University):
The forcability problem
We consider the following version of the Entscheidungsproblem : given an infinitary propositional
formula φ and a class of forcing notions K,
when can we add a satisfying assignment of φ by a forcing in K.
We are mainly interested in the case K is the class of proper, semiproper, or stationary
set preserving forcings.
For each of these classes, given a formula φ, we formulate a two person
infinite game GK,φ such that the desired poset exists if and only
if player 2 has a winning strategy in this game.
We also give sufficient conditions for the existence of such strategies.
As an application we sketch a somewhat different proof of the Aspero-Schindler theorem
stating that MM++ implies Woodin’s axiom (*).
This is joint work with my PhD student Obrad Kasum.
2025-10-21 - Jörg Brendle (Kobe University):
Cardinal invariants related to quotients by MAD families
Given a MAD family A, the quotient P(ω)/I(A), where I(A) is the ideal
generated by A, shares many properties of the algebra P(ω)/Fin. We investigate
cardinal invariants of such quotients and relate them to classical cardinal invariants.
This is joint work with Hiroaki Minami and with Yhon Castro, Michael Hrusak, and
Diego Mejia.
2025-10-14 - Mateusz Lichman (Łódź University of Technology):
On generalizations of Scott analysis
In 1965, D. Scott proved that for every countable structure of a countable language there
is a sentence of infinitary logic that describes it up to isomorphism. In order to obtain
this result, Scott developed what is now known as the Scott analysis: a way of approximating
the (analytic) isomorphism relation via a descending sequence of Borel equivalence relations.
We present a new way of approximating abstract equivalence relations on Polish spaces that
was introduced by S. Solecki and compare it with other known generalizations of Scott analysis,
in particular with metric Scott analysis defined in [I. Ben Yaacov, M. Doucha, A. Nies, T. Tsankov,
Metric Scott analysis, Advances in Mathematics 318 (2017) 46-87].
2025-10-07 - Andrej Dujella (University of Zagreb):
Diophantine m-tuples and elliptic curves
2025-10-07 - Arijeet Mishra:
HOD Conjecture
The HOD conjecture is a central problem in inner model theory which is concerned
with the closeness between HOD and V. In recent years, a lot of progress has been
made in this area. Especially, its connection with large cardinals. In this talk,
I will give a historical overview of the HOD conjecture and also its connection with
the HOD-Berkeley cardinal, upon which my research project is based.
2025-09-30 - Dorota Lesner:
I-closed sets
Zbiór A jest I-domknięty w przestrzeni X, gdy dla dowolnego I-zbieżnego ciągu zawartego w A, jego I-granica również należy do A. Pokażemy jaki warunek musi spełniać ideał I aby suma dwóch dowolnych zbiorów I-domkniętych również była takim zbiorem. Następnie przyjrzymy się przykładom ideałów, dla których ten warunek (nie) jest spełniony.
Abstract:
A set A is I-closed in a topological space X if the I-limit of any I-convergent sequence in A belongs to A.
I will show for which ideals the union of two I-closed sets is I-closed.
Next, I will present examples of ideals for which the above mentioned condition is (is not) satisfied.
2025-09-23 - Agnieszka Widz
(Łódź University of Technology):
Grafy losowe
Graf Rado (znany również jako graf losowy) to szczególny graf przeliczalny o wielu zaskakujących własnościach:
z prawdopodobieństwem 1 otrzymuje się go w najprostszej naturalnej procedurze losowania grafu na liczbach
naturalnych, a ponadto jest jedynym (z dokładnością do izomorfizmu) grafem przeliczalnym, który spełnia pewną silną
własność rozszerzania. W szczególności zawiera kopie wszystkich grafów przeliczalnych jako podgrafy indukowane.
Przez długi czas wydawało się, że temat losowania nieskończonych grafów został już wyczerpany, napisał tak np. Erdős
- jednak okazuje się, że wciąż kryje on ciekawe i zaskakujące możliwości.
W referacie przedstawię modyfikację klasycznego modelu losowania grafów poprzez użycie przeliczalnie wielu niesymetrycznych monet. W zależności od rozkładów prawdopodobieństwa przypisanych tym monetom, otrzymujemy różne klasy grafów losowalnych. Opowiem o warunkach, w których jedynym możliwym wynikiem losowania (z prawdopodobieństwem 1) jest graf Rado, oraz o takich, które pozwalają uzyskać znacznie szerszą i bardziej zróżnicowaną rodzinę grafów. Na zakończenie przedstawię również kolejny dowód potwierdzający wyjątkową „wszechobecność” grafu Rado.
Przedstawione będą wyniki wspólne z Jarosławem Swaczyną, Ziemowitem Kostaną i Leonardo Coregliano, część z nich pochodzi z pracy „How to get the Random Graph with non-uniform probabilities?” Electron. J. Combin. 32 (2025), no. 2, Paper No. 2.45, 8 pp.
2025-07-08 - Katarzyna Kowalik (University of Warsaw):
Reverse Mathematics of Ramsey-theoretic statements over a weaker base theory
Reverse mathematics is a programme in mathematical logic whose aim is to classify theorems
of ordinary mathematics according to their logical strength. Typically, one formalizes
a given theorem in the language of second-order arithmetic and then, working over a fixed
base theory, tries to prove implications and nonimplications between the theorem and some
well-understood arithmetical axioms.
One of the most interesting and difficult to analyse theorems in reverse mathematics is
Ramsey’s theorem for pairs and two colours (RT22),
which says that for every colouring of unordered pairs of natural numbers with two colours
there exists an infinite set on which the colouring is constant. In the first part of the
talk, I will give a brief introduction to the framework of reverse mathematics and discuss
classical results on RT22
over the usual base theory RCA0. Then, I will present our main results
about RT22
and some related combinatorial principles over a weaker set of axioms which
allows for a finer analysis of these theorems.
Joint work with Marta Fiori Carones, Leszek Kołodziejczyk and Keita Yokoyama.
2025-07-02 - Umutcan Kaya:
Gödel's Program and Generic Absoluteness
Gödel and Cohen revealed the limitations of formal systems like ZFC in settling certain mathematical statements
such as the Continuum Hypothesis. Then Gödel proposed a program to identify new axioms capable of resolving such
independent questions. In modern set theory, this has led to the study of generic absoluteness — the invariance
of truth under forcing extensions. This talk outlines the framework of Gödel’s program with emphasis on generic
absoluteness, highlighting results by Shoenfield, Woodin, and Sargsyan that connect large cardinals, determinacy,
and inner model theory to this goal.
2025-06-24 - Marcin Sabok (McGill University):
Bowen's Problem 32 and the conjugacy problem for systems with specification
We show that Rufus Bowen’s Problem 32 on the classification of symbolic systems with the specification property does
not admit a solution that would use concrete invariants. To this end, we construct a class of symbolic systems with
the specification property and show that the conjugacy relation on this class is too complicated to admit such
a classification. More generally, we gauge the complexity of the classification problem for symbolic systems
with the specification property. Along the way, we also provide answers to two questions related to the classification
of pointed systems with the specification property: to a question of Ding and Gu related to the complexity of
the classification of pointed Cantor systems with the specification property and to a question of Bruin and Vejnar
related to the complexity of the classification of pointed Hilbert cube systems with the specification property.
This is joint work with Konrad Deka, Dominik Kwietniak and Bo Peng.
2025-06-10 - Michał Pawlikowski (Łódź University of Technology):
Scales and combinatorial covering properties
A 𝕓-scale set is a subset of P(ω) of the form {xα : α < 𝕓} ∪ Fin,
where {xα : α < 𝕓} is an
unbounded set in [ω]ω and for all α < β we have xα ≤* xβ .
These sets play a crucial role in the investigation of combinatorial covering properties. Bartoszyński and Shelah
showed that each 𝕓-scale set is Hurewicz but not σ-compact which is a counterexample
in ZFC for Hurewicz’s conjecture. Under additional set-theoretical assumptions, by the
results of Bartoszyński, Tsaban and Weiss all finite powers of a 𝕓-scale set are Rothberger
and Hurewicz.
Recently, 𝕓-scale sets and their generalizations using filters were intensively investigated
in products with spaces having Hurewicz, Scheepers or Menger covering properties. Thus
far, another classical properties from the second row of the Scheepers Diagram have not
been considered in this context. We present new results in this field, in particular we
show that in the Miller model a product space of two 𝕕-concentrated sets has a strong
covering property S1(Γ, Ω). We also provide counterexamples in products to demonstrate
limitations of used methods.
The research was supported by the National Science Center, Poland under Weave-UNISONO
grant Set-theoretical aspects of topological selections 2021/03/Y/ST1/00122.
2025-06-03 - Klaudiusz Czudek (Gdańsk University of Technology):
The EVP process in quasi periodic environment
I am going to discuss the ergodic properties (e.g. the number of invariant measures) of the iterated function system
composed of circle rotations applied randomly. Those depend on the number-theoretic properties of the angle of rotation.
I am going to describe briefly how that iterated function system arises naturally in the study of random walks in random environment
as the environment viewed by the particle process (EVP).
2025-05-27 - Arturo Martínez-Celis (Wrocław University):
The ideal of I-compact sets
Given an ideal I on the natural numbers, the ideal of I-compact sets is the
σ-ideal generated by the infinite products of elements of I
(as an example, the usual ideal of compact sets is the ideal generated by
the infinite products of elements of Fin). In this talk, we will discuss
the properties of these ideals, calculate their cardinal invariants and
see their properties and relations in between different models of set theory.
2025-05-20 - Izabella Abraham (Transilvania University of Braşov):
The invariant measure for an at most countable topological generalized iterated function system
This talk is concerned with the existence and uniqueness of the invariant measure for generalized iterated function systems
consisting of an at most countable number of maps, in the context of Hausdorff topological spaces. More precisely, we show
that, given a Hausdorff space X, any at most countable topological generalized iterated function system on X, endowed with
a corresponding family of probabilities, admits a unique invariant measure, that is, a compactly-supported Radon probability
measure on X, which is the unique fixed point of the generalized Markov operator and whose support is the attractor of the
system. At the end of the talk, we discuss the topological nature of the invariant measure.
2025-05-13 - Raul Figueroa-Sierra (Andes University in Bogotá):
Nowhere Dense Ideals and the Category Dichotomy
The aim of this talk is to provide a construction of an ideal that fails the Category Dichotomy in the framework of ZFC; that is,
an ideal which is both Cohen-indestructible and weakly selective. The construction arises from the study of ideals nwd(X) of nowhere
dense subsets of a countable topological space X. We analyze how topological properties of X translate into combinatorial properties
of the associated ideal nwd(X). In particular, we identify sufficient conditions on X ensuring that nwd(X) simultaneously satisfies
both Cohen-indestructibility and weak selectivity, thus providing a counterexample to the Category Dichotomy. If time permits, we
exhibit a space introduced by A. Dow that fulfills these conditions.
2025-05-06 - Krzysztof Caban (Łódź University of Technology):
Topological approach to fuzzy iterated function systems
During the talk, we will take a closer look at a method to connect topological and fuzzy versions of
iterated function systems theory. We begin by briefly recalling the notions of multimetric spaces and
IFSs in this setting, as well as some fuzzy IFS theory. We study a natural way to extend fuzzy approach
onto multimetric spaces. Furthermore, we take a closer look at the topology obtained in this way and compare
it to different examples (uniform topology and identification of a fuzzy set with its hypograph). Finally, we
examine the existence of an attractor in this context.
2025-04-15 - Filip Strobin:
Various generalizations of iterated function systems
During my talk I will present several generalizations of classical notion of an iterated function system.
Originally, iterated function systems (IFSs for short) are finite families F={f1,...,fn} of continuous selfmaps of a metric space X.
The classical Hutchinson theorem from early 80's states that IFSs on complete metric spaces that consists of Banach contractions generates unique invariant
compact sets A (called as attractors), meaning that A = f1[A] ∪ ... ∪ fn[A].
Many classical fractal sets are IFS attractors and Hutchinson theorem is one of the most natural tools to construct fractals.
During my talk I will introduce or recall some extensions of the framework of iterated function systems.
At first I will show how to handle the IFS theory for systems of selfmaps of topological spaces.
In particular, I will present a topological contractivity condition that is sufficient for existence of attractors,
and I will explain the relationship between this condition and contractivity w.r.t. families of pseudometric.
Then I will recall the notion of fuzzy IFS. In this framework, attractors are certain fuzzy sets generated by appropriately defined
fuzzy version of the Hutchinson operator that transforms fuzzy sets.
Finally, I will say few words about generalized IFSs in the sense of Miculescu and Mihil. In this approach, selfmaps of a metric
space are replaced by maps f1, ..., fn defined on a finite Cartesian product Xm of a metric space and with values
in X. In particular, invariance w.r.t. family of such maps means A = f1[Am] ∪ ... ∪ fn[Am].
The presented notions will give a background for forthcoming seminars, in which more concrete issues within them will be discussed.
2025-04-08 - Jacek Tryba:
Thin, almost thin and lacunary sets and ideals generated by them
2025-04-01 - Jacek Tryba:
Thin, almost thin and lacunary sets and ideals generated by them
2025-03-25 - Daria Perkowska (Wrocław University of Science and Technology): Operation * and microscopic sets
During my talk, I will provide general remarks on the * operation and demonstrate when,
for some ideal I, we have I=I**. I will also present the Galvin-Mycielski-Solovay Theorem
on Cantor space. Then, I will explore the structure of microscopic and porous sets
on 2ω and discuss how they are related with respect to the * operation.
2025-03-18 - Jacek Tryba:
Coanalyticity of Hindman like ideals
2025-03-11 - Jakub Konieczny (University of Oxford):
Sparse generalised polynomials
Generalised polynomials are expressions built up from the usual polynomials with the use of the floor function and the basic arithmetic operations
of addition and multiplication. In contrast with the usual polynomials, their generalised counterparts can be bounded or even finitely-valued,
and can vanish almost everywhere, without being constant. By a sparse generalised polynomial set we mean a set E of integers such that the indicator
function 1E is a generalised polynomial and the natural density d(E) is zero. Together with Jakub Byszewski, in a series of papers spread
over several years, we investigated sparse generalised polynomial sets. In the positive direction, we obtained several surprising examples of sparse
generalised polynomial sets. These include: any subset of the Fibonacci numbers, sets of values of linear recurrence sequences satisfying certain
algebraic constraints, and all sets whose elements grow at least doubly exponentially. In the negative direction, we showed that a sparse generalised
polynomial set cannot contain an IP set (the sumset of an infinite set) nor a geometric progression. During the talk, I will provide an overview of
these results and discuss the ideas behind (some of) their proofs.
2025-01-28 -
Adam Kwela:
Zoo of filter Schauder bases
2025-01-21 -
Adam Kwela:
Zoo of filter Schauder bases
2025-01-14 - Tomasz Żuchowski (Wrocław University):
Ideals on ω and the Nikodym property
For a free filter F on ω, we consider the space NF=ω ∪ {pF}, where every element of ω is isolated and
open neighborhoods of pF are of the form A∪{pF} for A∈F.
In this talk we will study the family AN of such ideals I on ω that the space NI* carries
an ``anti-Nikodym'' sequence of measures - related to destroying the Nikodym property of Boolean algebras.
We'll show a characterization that I∈AN ⇔ there exists a density submeasure φ on ω such that φ(ω)=∞ and I⊂ Exh(φ).
Then we'll present a short proof that I∈AN ⇔ I is contained in a summable ideal.
We will mention results about the cofinal structure of the family AN ordered by the Katetov order ≤K.
We will also show connections of the class AN with the family of totally bounded ideals,
in particular the construction of continuum pairwise non-isomorphic non-pathological ideals which are not in
AN but are also not totally bounded.
2024
2024-12-17 -
Piotr Szuca:
Ramsey properties of sequences indexed by sets
2024-12-10 -
Piotr Szuca:
Ramsey properties of sequences indexed by sets
2024-12-05 -
Aleksander Cieślak (Wrocław University of Science and Technology):
Splitting ideal and antichains of P(ω)/I
2024-12-03 -
Ziemowit Kostana (Institute of Mathematics of the Czech Academy of Sciences):
Entangled linear orders and their variants
2024-11-26 -
Piotr Borodulin-Nadzieja (Wrocław University):
How to upgrade ultrafilters to measures
2024-11-19 -
Piotr Szuca:
Ramsey properties of sequences indexed by sets
2024-11-05 -
Andrzej Nowik:
The union of three ideals
2024-10-29 -
Jacek Tryba:
Nonpathology of van der Waerden ideal
2023-03-07 - Jacek Tryba: Katětov order on Borel ideals
2023-02-28 - Jacek Tryba: Katětov order on Borel ideals
2023-02-21 - Jan Kostrzon (University of Warsaw): Diamond in L[U] with short introduction to iterated ultrapowers.
2023-01-17 - Grigor Sargsyan (Institute of Mathematics of the Polish Academy of Sciences): omega strongly measurable cardinals in Pmax extensions of models of AD
2023-01-10 - Diana Montoya (University of Vienna): Maximal independence and singulars
2022
2022-12-13 - Wojciech Wołoszyn (University of Oxford): Modal logic: a unified approach to category theory and model theory
2022-12-06 - Krzysztof Kowitz: A unified approach to Hindman and van der Waerden spaces
2022-11-29 - Krzysztof Kowitz: A unified approach to Hindman and van der Waerden spaces
2022-11-22 - Jacek Gulgowski: Compactness in normed spaces: a unified approach through semi-norms
2022-11-15 - Jacek Tryba: Rapid ultrafilters and ideal convergence of series
2022-11-08 - Jacek Tryba: Rapid ultrafilters and ideal convergence of series
2022-10-25 - Jacek Tryba: Rapid ultrafilters and ideal convergence of series
2022-10-18 - Adam Kwela: On an infinite game related to I-ultrafilters
2022-10-11 - Piotr Szuca: Turnpike theorem without assumption of uniqueness
2022-07-11 - Ondřej Zindulka (Czech Technical University in Prague): Meager-additive sets and topological diagonalization
2022-06-28 - Rafał Filipów: Characterizing existence of certain ultrafilters
2022-06-21 - Rafał Filipów: Characterizing existence of certain ultrafilters
2022-06-14 - Rafał Filipów: Characterizing existence of certain ultrafilters
2022-06-07 - Krzysztof Kowitz: Characterizing existence of certain ultrafilters
2022-05-24 - Szymon Żeberski (Wrocław University of Science and Technology): Inscribing rectangles into big sets
2022-05-17 - Krzysztof Kowitz: Characterizing existence of certain ultrafilters
2022-05-12 - Filip Strobin (Łódź University of Technology): Attractors of non-contractive IFSs (iterated function systems)
2022-05-05 - Filip Strobin (Łódź University of Technology): Gently introduction to Hutchinson-Barnsley theory of fractals
2022-04-26 - Tomasz Natkaniec: Almost continuous Sierpiński-Zygmund functions under different set theoretical assumptions
2022-04-12 - Xi He (Sichuan University): The Borel complexity of ideal limit points
2022-03-29 - Wojciech Wołoszyn (University of Oxford): The resurrection axiom and the mantle
2022-03-22 - Tomasz Natkaniec: Almost continuous Sierpiński-Zygmund functions under different set theoretical assumptions
2022-03-15 - Jacek Tryba: Filters and statistical measures
2022-03-08 - Paolo Leonetti (Bocconi University in Milano): Tauberian theorems for ordinary convergence
2022-01-18 - Adam Kwela: On a conjecture of Debs and Saint Raymond
2022-01-11 - Adam Kwela: On a conjecture of Debs and Saint Raymond
2021
2021-12-21 - Adam Kwela: Yet another ideal version of the bounding number
2021-12-14 - Rafał Filipów: Yet another ideal version of the bounding number
2021-12-07 - Rafał Filipów: Yet another ideal version of the bounding number
2021-11-16 - Martina Iannella (University of Udine): Convex embeddability on linear/circular orders and connections to knot theory
2021-11-09 - Justyna Poprawa (University of Łódź): Local aspects of entropy and chaos of discrete dynamical systems.
2021-11-02 - Grigor Sargsyan (Institute of Mathematics of the Polish Academy of Sciences): Generic absoluteness for universally Baire sets
2021-10-26 - Grigor Sargsyan (Institute of Mathematics of the Polish Academy of Sciences): Generic absoluteness for universally Baire sets
2021-10-19 - Piotr Szuca: Pointwise continuity, pointwise discontinuity and Namioka’s theorem
2021-10-12 - Piotr Szuca: Pointwise continuity, pointwise discontinuity and Namioka’s theorem
2021-06-01 - Paweł Klinga: σ-porosity of certain known ideals
2021-05-25 - Jarosław Swaczyna (Łódź University of Technology and Institute of Mathematics of the Czech Academy of Sciences): Polish space of separable Banach spaces and its application to continuity of filter-projections
2021-05-18 - Krzysztof Kowitz: Hindman spaces which are not I-spaces
2021-04-13 - Jacek Marchwicki (University of Warmia and Mazury in Olsztyn): Recovering a purely atomic finite measure from its range
2021-03-30 - Rafał Filipów: The cardinal characteristics of ideals in-between ideals ED and Fin⊗Fin
2021-03-23 - Rafał Filipów: The Katětov order structure of ideals in-between ideals ED and Fin⊗Fin
2021-03-16 - Marek Balcerzak (Łódź University of Technology): Families of equi-Borel 1 functions.
2021-03-09 - Rafał Filipów: The Katětov order structure of ideals in-between ideals ED and Fin⊗Fin
2021-03-02 - Rafał Filipów: The Katětov order structure of ideals in-between ideals ED and Fin⊗Fin
2021-02-23 - Paolo Leonetti (Bocconi University in Milano): Turnpike theory.
2021-01-19 - Wojciech Wołoszyn (University of Oxford): Modal model theory
2021-01-12 - Jacek Tryba: Ideals of nowhere dense sets on N
2020
2020-12-15 - Pratulananda Das (Jadavpur University in Kolkata): Generating uncountable subgroups of the circle group by certain modes of convergence
2020-12-08 - Jaroslav Šupina (University of Vienna and Pavol Jozef Šafárik University in Košice): Ideal Frechet-Urysohn property of a space of continuous functions
2020-11-24 - Tomasz Natkaniec: Lineability of families of nonmeasurable functions of 2 variables
2020-11-03 - Bartosz Kamedulski: εω order on natural
2020-11-17 - Tomasz Natkaniec: Lineability of families of nonmeasurable functions of 2 variables
2020-11-10 - Bartosz Kamedulski: εω order on naturals
2020-10-27 - Piotr Szuca: Equi-Baire one family of functions
2020-10-20 - Piotr Szuca: Equi-Baire one family of functions
2020-10-06 - Piotr Szuca: Equi-Baire one family of functions
2020-04-01 - Dr. Bìngdú (Wuhan University): Cardinal Operations Ranging Over Natural Alexandrov-Vinogradov Injective Relations Using Superposition
2020-02-25 - Piotr Sworowski (Casimir the Great University in Bydgoszcz): On uniform limits of Baire**1 functions
2020-02-18 - Krzysztof Kowitz: Arithmetic progressions in lacunary sets
2020-01-21 - Krzysztof Kowitz: van der Waerden spaces and Hindman spaces are not the same
2020-01-14 - Piotr Nowakowski (Łódź University of Technology): Microscopic sets among symmetric Cantor sets
2020-01-07 - Jacek Tryba: Different kinds of density ideals
2019
2019-12-17 - Stanisław Kowalczyk (Pomeranian University in Słupsk): On sets of points of quasicontinuity and porouscontinuity
2019-12-10 - Piotr Szuca: ω-diagonalizability of Fσ filters
2019-12-03 - Franciszek Prus-Wiśniowski (University of Szczecin): The arithmetic sums of central Cantor sets
2019-11-26 - Piotr Szuca: ω-diagonalizability of Fσ filters
2019-11-19 - Piotr Szuca: ω-diagonalizability of Fσ filters
2019-11-05 - Adam Kwela: Generalized density ideals versus density-like ideals
2019-10-29 - Adam Kwela: Generalized density ideals versus density-like ideals
2019-10-22 - Adam Ostaszewski (London School of Economics): Multivariate regular variation and Popa homomorphisms
2019-10-15 - Eliza Jabłońska (Pedagogical University of Cracow): Generically Haar-small sets in abelian Polish groups
2019-10-08 - Arturo Martínez-Celis (Institute of Mathematics of the Polish Academy of Sciences): P+-filters of finite sets
2019-09-27 - Ziemowit Kostana (University of Warsaw and Institute of Mathematics of the Czech Academy of Sciences): On big subgroups evading small sets
2019-06-04 - Rafał Filipów: Ideals generated by families of sequences of natural numbers - topological complexity
2019-05-28 - Adam Ostaszewski (London School of Economics): The Steinhaus support: Beyond the confines of Haar and Cameron-Martin
2019-05-21 - Jaroslav Šupina (Pavol Jozef Šafárik University in Košice): On ideal cardinal invariants and singular sets
2019-05-14 - Michał Banakiewicz (West Pomeranian University of Technology in Szczecin): The set of subsums of the Guthrie-Nymann-Jones series
2019-05-07 - Rafał Filipów: Ideals generated by families of sequences of natural numbers - basic properties
2019-04-25 - Wojciech Wołoszyn (University of Oxford): On the multiverse, potentialism, and implicit actualism
2019-04-16 - Piotr Szuca: The structure of equicontinuous maps
2019-04-09 - Tomasz Natkaniec: Different notions of Sierpiński-Zygmund functions
2019-04-02 - Tomasz Natkaniec: Different notions of Sierpiński-Zygmund functions
2019-03-26 - Jacek Tryba: A proof of a sumset conjecture of Erdős
2019-03-19 - Adam Kwela: Nonmeasurable subgroups of compact groups
2019-03-12 - Bartosz Kamedulski: G-spaces, equivariant degree and its product property
2019-03-05 - Andrzej Nowik: Ideals of nowhere dense sets in some topologies on positive integers
2019-02-26 - Andrzej Nowik: Ideals of nowhere dense sets in some topologies on positive integers
2019-02-21 - Adam Ostaszewski (London School of Economics): Kendall’s sequential characterization of regular variation: Category versus measure
2019-02-19 - Piotr Sworowski (Casimir the Great University in Bydgoszcz), Comparison of some trigonometric integrals
2019-01-22 - Edward Grzegorek: On σ-algebras closed under Souslin’s operation and Stanisław Saks theorem
2019-01-15 - Piotr Sworowski (Casimir the Great University in Bydgoszcz), Comparison of some trigonometric integrals
2018
2018-12-18 - Gertruda Ivanova (Pomeranian University in Słupsk): Comparison of some families of real functions in porosity terms
2018-12-11 - Jacek Tryba: A note on nonregular matrices and ideals associated with them
2018-12-04 - Marcin Szyszkowski: Matrices of projections and their diagonals - how to connect them in measurable way
2018-11-27 - A seminar dedicated to the 95th birthday of Professor Lipiński
2018-11-20 - Edward Grzegorek: On σ-algebras closed under Souslin’s operation
2018-11-13 - Rafał Filipów: Abstract densities and ideals of sets
2018-11-06 - Stanisław Kowalczyk (Pomeranian University in Słupsk): Multiplication in the space of functions of bounded variation
2018-10-30 - Stanisław Kowalczyk (Pomeranian University in Słupsk): Multiplication in the space of functions of bounded variation
2018-10-23 - Adam Ostaszewski (London School of Economics): Centenary of the Steinhaus(-Weil) Theorem: A sneak preview
2018-10-16 - Adam Kwela - Marcin Staniszewski: Size of the set of attractors for iterated function systems
2018-10-09 - Adam Kwela - Marcin Staniszewski: Size of the set of attractors for iterated function systems
2018-06-19 - Paweł Klinga: Attractors for iterated function systems form an Fσ set
2017-11-07 - Piotr Szuca: On Darboux-Baire one composition problem
2017-10-24 - Adam Ostaszewski (London School of Economics): Additivity and subadditivity in the light of asymptotic group action
2017-10-17 - Tomasz Natkaniec: Perfectly everywhere surjective but not Jones functions
2017-10-10 - Tomasz Natkaniec: Perfectly everywhere surjective but not Jones functions
2017-07-20 - Wiesław Kubiś (Institute of Mathematics of the Czech Academy of Sciences and Cardinal Stefan Wyszyński University in Warsaw): Universal homogeneous probability measure on the Cantor set
2017-06-13 - Pratulananda Das (Jadavpur University in Kolkata): Some remarks on open covers and selection principles using ideals
2017-06-06 - Michał Małafiejski (Gdańsk University of Technology): Generalization of Hales-Jewett theorem
2017-05-23 - Jacek Tryba: Dense difference sets and their combinatorial structure
2017-05-16 - Jacek Tryba: Various problems on densities
2017-05-09 - Jacek Tryba: Various problems on densities
2017-04-25 - Marek Balcerzak (Łódź University of Technology): Baire category of ideal convergent subseries and permutations
2017-04-11 - Adam Ostaszewski (London School of Economics): Walk on the real line: stable distributions versus functional equations
2017-04-04 - Michał Małafiejski (Gdańsk University of Technology): Generalization of Hales-Jewett theorem
2017-03-28 - Michał Małafiejski (Gdańsk University of Technology): Generalization of Hales-Jewett theorem
2017-02-28 - Tomasz Natkaniec: Pointwise limits of sequences of Świątkowski functions
2017-02-21 - Tomasz Natkaniec: Pointwise limits of sequences of Świątkowski functions
2017-02-14 - Adam Ostaszewski (London School of Economics): Category-measure duality: convexity, mid-point convexity and Berz sublinearity
2017-01-24 - Tomasz Natkaniec: Pointwise limits of sequences of Świątkowski functions
2017-01-17 - Waldemar Sieg (Casimir the Great University in Bydgoszcz): P-spaces and an unconditional closed graph theorem
2017-01-10 - Waldemar Sieg (Casimir the Great University in Bydgoszcz): P-spaces and an unconditional closed graph theorem
2016
2016-12-20 - Marta Frankowska: Symmetric density points in the Cantor set
2016-12-06 - Piotr Szuca: On extensions of asymptotic density
2016-11-29 - Jacek Tryba: On extensions of asymptotic density
2016-11-22 - Nikodem Mrożek: Katětov and Katětov-Blass orders on Fσ-ideals
2016-11-15 - Jacek Tryba: Ideal convergence versus matrix summability
2016-11-08 - Rafał Filipów: Intersection of matrix summability methods
2016-10-25 - Adam Ostaszewski (London School of Economics): On theorem of Effros about micro-transitive actions on Baire groups
2016-10-18 - Rafał Filipów: Intersection of matrix summability methods
2016-10-11 - Rafał Filipów: Intersection of matrix summability methods
2016-06-14 - Klaudiusz Czudek: Bernstein and Kantorovitch polynomials
2016-06-07 - Marcin Szyszkowski: Separating sets with Gδ (and Fσ) sets
2016-05-31 - Klaudiusz Czudek: Superposition operators in the space of functions of bounded variation
2016-05-24 - Julia Wódka (Łódź University of Technology): Uniform limits of sequences of Świątkowski functions
2016-05-17 - Nikodem Mrożek: Dominated Convergence and Egorov Theorems for Filter Convergence
2016-05-10 - Nikodem Mrożek: Dominated Convergence and Egorov Theorems for Filter Convergence
2016-04-26 - Paulina Szczuka (Casimir the Great University in Bydgoszcz): Topological and algebraic properties of Darboux-like and pointwise discontinuous functions
2016-04-19 - Jacek Tryba: Darboux property for weighted uniform densities
2016-04-12 - Jacek Tryba: Darboux property for weighted uniform densities
2016-04-05 - Adam Ostaszewski (London School of Economics): On the Steinhaus property
2016-03-22 - Jacek Tryba: Ideal invariant injections
2016-03-15 - Adam Kwela: Homogeneous and hereditarily homogeneous ideals
2016-03-08 - Paulina Szczuka (Casimir the Great University in Bydgoszcz): Topologies on the integers generated by arithmetic progressions
2016-03-01 - Adam Kwela: Ideal invariant injections with large sets of fixed points
2016-02-16 - Waldemar Sieg (Casimir the Great University in Bydgoszcz): Extensions of some Baire one functions
2016-01-19 - Waldemar Sieg (Casimir the Great University in Bydgoszcz): Extensions of some Baire one functions
2016-01-12 - Marcin Staniszewski: Quasi-normal convergence of sequences of quasi-continuous functions
2016-01-05 - Marcin Staniszewski: Quasi-normal convergence of sequences of quasi-continuous functions
2015
2015-12-15 - Marcin Staniszewski: Quasi-normal convergence of sequences of quasi-continuous functions
2015-12-08 - Marcin Staniszewski: Quasi-normal convergence of sequences of quasi-continuous functions
2015-12-01 - Marcin Staniszewski: Quasi-normal convergence of sequences of quasi-continuous functions
2015-11-24 - Marcin Staniszewski: Quasi-normal convergence of sequences of quasi-continuous functions
2015-11-17 - Rafał Filipów: Two ideals not fulfilling Fatou’s lemma: Solecki’s ideal and finite coloring ideal
2015-11-10 - Marcin Staniszewski: Quasi-normal convergence of sequences of continuous functions
2015-11-03 - Marcin Staniszewski: Quasi-normal convergence of sequences of continuous functions
2015-10-27 - Adam Ostaszewski (London School of Economics): The sound of silence: filtering and optimal censorship in the market (Krzyk ciszy: filtrowanie i optymalna cenzura w rynkach finansowych)
2015-10-20 - Jacek Tryba: A matrix characterization of statistical convergence (Mazur’s problem from The Scottish Book)
2015-10-13 - Jacek Tryba: On modified Olivier’s theorem for some idelas
2015-10-05 - Szymon Głąb (Politechnika Łódźka): Duże wolne podgrupy grup automorfizmów przestrzeni ultrahomogenicznych
2015-06-09 - Marcin Staniszewski: O zbieżności ideałowej
2015-06-09 - Jacek Tryba: O pewnym rodzaju zbieżności ciągów zdefiniowanym przy pomocy f-gęstości
2015-06-02 - Marcin Staniszewski: O zbieżności ideałowej
2015-05-26 - Adam Ostaszewski (London School of Economics): Homeomorphisms from functional equations in probability
2015-05-19 - Marcin Staniszewski: O zbieżności ideałowej
2015-05-12 - Marcin Staniszewski: O zbieżności ideałowej
2015-05-05 - Adam Kwela: O addytywności zbiorów mikroskopijnych
2015-04-28 - Adam Kwela: O addytywności zbiorów mikroskopijnych
2015-04-21 - Piotr Szuca: Uogólnienie gęstości asymptotycznej
2015-04-14 - Piotr Szuca: Uogólnienie gęstości asymptotycznej
2015-03-31 - Piotr Szuca: Uogólnienie gęstości asymptotycznej
2015-03-24 - Paweł Klinga: Ideałowa wersja twierdzenia Riemanna
2015-03-17 - Jacek Tryba: Ideałowa zbieżność szeregów liczbowych
2015-03-10 - Jacek Tryba: Ideałowa zbieżność szeregów liczbowych
2015-03-03 - Paweł Barbarski: Zrandomizowane twierdzenie Szarkowskiego
2015-02-24 - Paweł Barbarski: Zrandomizowane twierdzenie Szarkowskiego
2015-01-27 - Paweł Barbarski: Zrandomizowane twierdzenie Szarkowskiego
2015-01-20 - Paweł Barbarski: Zrandomizowane twierdzenie Szarkowskiego