impan seminar:

working group in applications of set theory



23.04.2015 at 13.15 room 105.

Marek Cuth (IM PAN): Do countable models of ZFC generate club of separable subspaces in a Banach space?

Abstract: First, I will briefly talk about separable reductions and try to explain why it is interesting to solve the problem from the title. Then, I will talk about some partial results and about the difficulities when trying to solve the problem in full generality. Separable reduction is a method of extension the validity of a statement from separable spaces to the nonseparable setting not involving the proof of the statement in the separable case. This method is based on a construction of a separable subspace with certain properties. One possibility of constructing a separable subspace of a Banach space X is to take countable model of ZFC (more precisely, of a finite fragment of ZFC), call it M, and then take the closure of the points from M which are in X. The question is, how good the family of so constructed separable subspaces can be. Namely, is it possible to find a family of countable models of ZFC in such a way that those subspaces will form a club?

Previous talks this semester:


Alternative activities










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 11.15-13.00 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:

  • Marek Cuth (WCMCS-IM PAN)
  • Michal Doucha (IMPACT/IM PAN)
  • Piotr Koszmider (IM PAN)
  • Gabriel Salazar (IM PAN)
  • Damian Sobota (Ph. D. student IM PAN)
  • Michał Świętek (Ph. D. student UJ/WCMCS-IM PAN)
  • Michał Wojciechowski (IM PAN)
Forthcoming talks:

  • 30.04 No seminar (A meeting of the Scientific Council takes place)