impan seminar:

working group in applications of set theory



23.05.2019 , 10.15, room 105,

Piotr Koszmider (IMPAN),

Title: Lifting uncountable combinatorics to the Banach space level: Banach spaces C(K) with few operators. Part 1.

Abstract: "This series of 4 talks will be a minicourse on Banach spaces of continuous functions which have few operators, projections, injections etc. In particular they can be indecomposable and nonisomorphic with their hyperplanes. To obtain this linear operator level rigidity one needs to construct compact Ks which are not only rigid in the usual sense, i.e., in terms of continuous mappings on K. One needs to deal with weak* continuous functions from K into the space M(K) of Radon measures on K, so the combinatorics of the constructions needs stronger conditions then for endo-rigid Boolean algebras or strongly rigid compact spaces. We will present main arguments leading to C(K)s with the required properties but the proofs of many lemmas will be omitted. The talks should be accessible to everyone with general analytic and topological background."

Previous talks this semester:


09.05.2019 , 10.15, room 105,

Arturo Martínez-Celis (IMPAN),

Title: Choice vs Determinacy

Abstract: "We will discuss the concept of infinite game and winning strategies and we will present some examples, theorems and applications to topology. In particular we will prove that every uncountable Borel set has a homeomorphic copy of the Cantor set. The axiom of determinacy (AD) states that for certain kind of games, the Gale-Stewart games, one player has always a winning strategy. The aim of this talk is to present the differences between the universes satisfying AD and the universes satisfying the axiom of choice."

26.04.2019 (Friday), 10.15, room 106,

Fulgencio Lopez (IMPAN),

Title: Compact extensions of first order logic, continuation from 16.04


Abstract: We aim to provide an exhaustive proof of the results of Keisler and Magidor and Malitz about the compactness of certain extensions of first order logic. Keisler's Theorem refers to the extension L(Q) where Q is the quantifier "There is an uncountable subset with a one dimensional property", similarly we can define Qn to be "There is an uncountable subset with an n-dimensional property". We will show that L(Q) is compact (Keisler's Theorem) and, assuming diamond, so is L(Qn:n∈ N) (Magidor and Malitz). We will also discuss why this framework can sometimes be useful for constructions of set theoretical structures.

16.04.2019 (Tuesday), 10.15, room 106,

Fulgencio Lopez (IMPAN),

Title: Compact extensions of first order logic


Abstract: We aim to provide an exhaustive proof of the results of Keisler and Magidor and Malitz about the compactness of certain extensions of first order logic. Keisler's Theorem refers to the extension L(Q) where Q is the quantifier "There is an uncountable subset with a one dimensional property", similarly we can define Qn to be "There is an uncountable subset with an n-dimensional property". We will show that L(Q) is compact (Keisler's Theorem) and, assuming diamond, so is L(Qn:n∈ N) (Magidor and Malitz). We will also discuss why this framework can sometimes be useful for constructions of set theoretical structures.








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: Thursdays 10.15-12.00 am, room 105, Sniadeckich 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:

  • Tomasz Kochanek (IM PAN/UW)
  • Ziemowit Kostana, doctoral student (UW)
  • Piotr Koszmider (IM PAN)
  • Fulgencio Lopez (IM PAN)
  • Arturo Martínez-Celis (IM PAN)
  • Marek Miarka, doctoral student (UW)
  • Damian Sobota (KGRC Vienna)
Forthcoming talks : Until May 9 the meetings of the seminar will take place at unusual times due to holidays and to the Scientific Council of the Institute.


  • 16.05: no seminar,
  • 23.05: Piotr Koszmider: minicourse on Banach spaces of continuous functions with few operators
  • 30.05: Piotr Koszmider: minicourse on Banach spaces of continuous functions with few operators
  • 06.06: Piotr Koszmider: minicourse on Banach spaces of continuous functions with few operators
  • 13.06: Piotr Koszmider: minicourse on Banach spaces of continuous functions with few operators