impan seminar:

working group in applications of set theory





8.10. 2026 at 10.15 am. Room 106.

Piotr Koszmider (IMPAN)
An Efimov space in the Cohen model.


Abstract: A compact Hausdorff space is called an Efimov space if it contains neither a nontrivial convergent sequence nor a copy of βN. Whether such a space can be constructed in ZFC remains a longstanding open problem. We will describe a (mostly folklore) construction of an Efimov space in a Cohen model, emphasizing the main combinatorial ideas and the way Cohen forcing is used to destroy all potential convergent sequences. The proof is via the Stone duality, i.e., we construct the Boolean algebra of all clopen subsets of the space.




Previous talks this semester:






Talks in the second semester of 2025-26.

Talks in the first semester of 2025-26.

Talks in the second semester of 2024-25.

Talks in the first semester of 2024-25.

Talks in the second semester of 2023-24.

Talks in the first semester of 2023-24.

Talks in the second semester of 2022-23.

Talks in the first semester of 2022-23.

Talks in the second semester of 2021-22.

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: Thursdays 10.15-12.00, room 106, Śniadeckich 8



Organizers: Piotr Koszmider (IMPAN) and Piotr Szewczak (MIM UW)


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:

Forthcoming talks:

  • 15.10 Grzegorz Wełyczko (PWr) will talk on the consistency of the nonexistence of universal structures of size continuum.