impan seminar:

working group in applications of set theory



No more seminars this semester

Previous talks this semester:

14.06.2022, Tuesday 13.15, room 403
Krzysztof Zakrzewski (MIM UW)

Elementary submodels and Corson-compact spaces.

Abstract: "We will present a characterisation of Corson-compact spaces using elementary submodels and use it to show a theorem proved earlier by Gul'ko stating that a Hausdorff continuous image of a Corson-compact space is Corson-compact."

31.05.2022, Tuesday 13.15, room 403
Jakub Andruszkiewicz (UW/IM PAN)

Countable support iterations of proper forcing notions.

Abstract: "We present a classical result concerning iterations of proper forcings, namely that the properness is preserved by countable support iterations. We will follow section 3 of "Tools for your forcing construction" by M. Goldstern."

24.05.2022, Tuesday 13.15, room 403
Piotr Koszmider (IM PAN)

Introduction to proper forcing and its applications, continuation.

Abstract: "In this introductory series of talks we will prove some basic properties of proper forcing, show fundamental examples and present some paradigmatic applications in the context of the proper forcing axiom using elementary submodels as side conditions."

17.05.2022, Tuesday 13.15, room 403
Piotr Koszmider (IM PAN)

Introduction to proper forcing and its applications, continuation.

Abstract: "In this introductory series of talks we will prove some basic properties of proper forcing, show fundamental examples and present some paradigmatic applications in the context of the proper forcing axiom using elementary submodels as side conditions."

10.05.2022, Tuesday 13.15, room 403
Piotr Koszmider (IM PAN)

Introduction to proper forcing and its applications.

Abstract: "In this introductory series of talks we will prove some basic properties of proper forcing, show fundamental examples and present some paradigmatic applications in the context of the proper forcing axiom using elementary submodels as side conditions."

26.04.2022, Tuesday 13.15, room 403
Kacper Kucharski (MIM UW)

Using elementary submodels in topology (continuation).

Abstract: "The talk will be focused on presenting so-called reflection results e.g., Dow's theorem: every nonmetrizable compact Hausdorff space contains a nonmetrizable subspace of cardinality ω1."

05.04.2022, Tuesday 13.15, room 403
Damian Sobota (KGRC Vienna)

Measures with the Additive Property and the random forcing

Abstract: "Let μ be a finitely additive probability measure on ω which vanishes on points, that is, μ({n})=0 for every n∈ω. It follows immediately that μ is not σ-additive, however it may be almost σ-additive in the following weak sense. We say that μ has the Additive Property, (AP) in short, if for every sequence (An) of pairwise disjoint subsets of ω there is a subset A such that An\A is finite for every n∈ω and μ(A)=Σn μ(An). Equivalently, for every decreasing sequence (An) of subsets of ω there is a subset A such that A\An is finite for every n∈ω and μ(A)=limn μ(An). The latter definition implies immediately that, e.g., an ultrafilter U on ω is a P-point if and only if the one-point measure δU has (AP). And similarly as in the case of P-points the existence of measures with (AP) is independent of ZFC.

During my talk I will discuss basic properties of (families of) measures with (AP) as well as show, at least briefly, that using old ideas of Solovay and Kunen one can obtain a non-atomic measure with (AP) in the random model. The latter result implies that in this model there exists a ccc P-set in ω*, which may be treated as a (weak) partial answer to the question asking whether there are P-points in the random model.

This is a joint work with Piotr Borodulin-Nadzieja.

29.03.2022, Tuesday 13.15, room 403
Kacper Kucharski (MIM UW)

Using elementary submodels in topology

Abstract: "The main goal of the talk is to present proofs of interesting topological theorems using elementary submodels. One theorem will be the classical Arhangel'skii's result which says that the cardinality of a compact Hausdorff first countable space is at most the continuum. The second part of the talk will be focused on presenting so-called reflection results e.g., Dow's theorem: every nonmetrizable compact Hausdorff space contains a nonmetrizable subspace of cardinality ω1"

22.03.2022, Tuesday 13.15, room 403
Kamil Ryduchowski (MIM UW)

Elementary submodels and infinitary combinatorics

Abstract: "We will present techniques of using elementary submodels as a tool in infinitary combinatorics. We shall show short, elegant proofs of, among others, the Delta-system lemma, the pressing-down lemma, Erdos-Dushnik-Miller theorem."

15.03.2022, Tuesday 13.15, room 403
Jakub Andruszkiewicz (UW/IM PAN)

The club principle and its connections to the diamond principle

Abstract: "The club principle was first introduced by Ostaszewski as a weakening of the diamond principle, as it plays a crucial role in his original construction of the Ostaszewski space. It is well-known that under CH those principles are equivalent and we will present a proof of this fact. We will also show by using an appropriate forcing extension that, as proven by Shelah, assuming CH is essential, i.e. it is consistent relative to ZFC that the club principle holds while the diamond principle does not."

8.03.2022, Tuesday 13.15, room 403
Piotr Koszmider (IM PAN)

The Ostaszewski space

Abstract: "We will present a construction of the classical Ostaszewski space. Like the construction of a Suslin tree, it is a paradigmatic construction which inspired diamond based arguments in diverse applications."








Talks in the first semester of 2021-22.

Talks in the second semester of 2020-21.

Talks in the first semester of 2020-21.

Talks in the second semester of 2019-20.

Talks in the first semester of 2019-20.

Talks in the second semester of 2018-19.

Talks in the first semester of 2018-19.

Talks in the second semester of 2017-18.

Talks in the first semester of 2017-18.

Talks in the second semester of 2016-17.

Talks in the first semester of 2016-17.

Talks in the second semester of 2015-16.

Talks in the first semester of 2015-16.

Talks in the second semester of 2014-15.

Talks in the first semester of 2014-15.

Talks in the second semester of 2013-14.

Talks in the first semester of 2013-14.

Talks in the second semester of 2012-13.

Talks in the first semester of 2012-13.

Talks in the second semester of 2011-12.

Talks in the first semester of 2011-12.

Time and place: Tuesdays 13.15-15.00 pm, room 403, Śniadeckich 8




The scope of the seminar: Set-theoretic combinatorial and topological methods in diverse fields of mathematics, with a special emphasis on abstract analysis like Banach spaces, Banach algebras, C*-algebras, Here we include both the developing of such methods as forcing, descriptive set theory, Ramsey theory as well as their concrete applications in the fields mentioned above.

Working group style: We will make efforts so that this seminar has more a working character rather than the presentation style. This means that we encourage long digressions, discussions, background preparations and participation of everyone. We would like to immerse ourselves into the details of the mathematical arguments studied. Also the talks are usualy devoted to research in progress or fascinating results leading to some project not yet resolved. While ready final results could be presented at other seminars at IM PAN or UW.

Participants this semester so far:

  • Jakub Andruszkiewicz, (PH.D. student UW/IMPAN)
  • Damian Głodkowski (PH.D. student UW/IMPAN)
  • Piotr Koszmider (IM PAN)
  • Kacper Kucharski (M.A. student UW)
  • Maciej Malicki (IM PAN)
  • Kamil Ryduchowski (M.A. student UW)
  • Krzysztof Zakrzewski (PH.D. student UW)
Forthcoming talks :

  • No more talks in this semester