impan seminar:

working group in applications of set theory




28.03.2023, Tuesday 10.15, room 403

Piotr Koszmider (IMPAN)

Title: Stepping-up with an Aronszajn tree and adding a Cohen real. Continuation.

Abstract: "We will discuss classical techniques involving almost coherent families of injections from countable ordinals into ω and adding a Cohen real. Applications will include: adding one Cohen real to any model produces a coloring with the Galvin property, Suslin tree and an entangled set of reals etc."



Previous talks this semester:



21.03.2023, Tuesday 10.15, room 403

Krzysztof Zakrzewski (MIMUW)

Title: An elementary proof of the Eberlein-Smulian theorem. Continuation.

Abstract: "We will give a brief proof of the Eberlein-Smulian theorem which says that for a subset of a Banach space endowed with the weak topology three conditions are equivalent, namely: conditional compactness, conditional sequential compactness and conditional countable compactness. The proof will use standard results from theory of Banach spaces, namely Alaoglu's theorem and the Hahn-Banach theorem.
The talk is based on the article "An Elementary Proof of Eberlein-Smulian Theorem" by Robert Whitley (Math. Ann. 1967)"


14.03.2023, Tuesday 10.15, room 403

Krzysztof Zakrzewski (MIMUW)

Title: An elementary proof of the Eberlein-Smulian theorem.

Abstract: "We will give a brief proof of the Eberlein-Smulian theorem which says that for a subset of a Banach space endowed with the weak topology three conditions are equivalent, namely: conditional compactness, conditional sequential compactness and conditional countable compactness. The proof will use standard results from theory of Banach spaces, namely Alaoglu's theorem and the Hahn-Banach theorem.
The talk is based on the article "An Elementary Proof of Eberlein-Smulian Theorem" by Robert Whitley (Math. Ann. 1967)"


7.03.2023, Tuesday 10.15, room 403


Piotr Koszmider (IMPAN)

Title: Stepping-up with an Aronszajn tree and adding a Cohen real.

Abstract: "We will discuss classical techniques involving almost coherent families of injections from countable ordinals into ω and involving adding a Cohen real. Applications will include: The existence of a strong Luzin set implies the existence of a coloring of pairs of ω1 with very strong multidimensional antiramsey properties; adding one Cohen real to any model produces a Suslin tree and produces an entangled set of reals etc."













Talks in the second 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: Tuesdays 10.15-12.00 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:

  • Tomasz Kochanek (MIM UW)
  • Piotr Koszmider (IM PAN)
  • Kacper Kucharski (M.A. student UW)
  • Kamil Ryduchowski (PH. D. student UW/IMPAN)
  • Zdeněk Silber (IM PAN)
  • Przemysław Wojtaszczyk (IM PAN)
  • Krzysztof Zakrzewski (PH.D. student UW)
Forthcoming talks :

  • 4.04. Zdenek Silber will talk about convex versions of coutable tightness.
  • 11.04 no seminar.