impan seminar:

working group in applications of set theory



15.11.2018. 10.15, room 105;
Fulgencio Lopez (IM PAN)
A capturing construction scheme from the diamond principle. Continuation from 8.11.2018.

Abstract: S. Todorcevic introduced the concept of a capturing construction scheme and showed it is consistent with the diamond principle. A construction scheme is a well-founded family of finite subsets of ω1. We give a quick presentation of the history and motivation for this tool and show that it follows from the diamond principle.

Previous talks this semester:

08.11.2018. 10.15, room 105;
Fulgencio Lopez (IM PAN)
A capturing construction scheme from the diamond principle.

Abstract: S. Todorcevic introduced the concept of a capturing construction scheme and showed it is consistent with the diamond principle. A construction scheme is a well-founded family of finite subsets of ω1. We give a quick presentation of the history and motivation for this tool and show that it follows from the diamond principle.

25.10.2018. 10.15, room 105;
Arturo Martínez-Celis (IM PAN)
On the Michael Space Problem

Abstract: A Lindelöf Topological space is Michael if it has non-Lindelöf product with the space of the irrational numbers. These kind of spaces were introduced by Ernest Michael in 1963 and it is still unknown if one can be constructed in ZFC. We will introduce the notion of Michael ultrafilter, which implies the existence of a Michael space. We will also discuss the relation between this kind of ultrafilters and some classical cardinal invariants and we will use this to study the behaviour of this notion in some models of set theory.

11.10.2018. 10.15, room 105;
Piotr Koszmider (IMPAN)
Uncountable constructions from CH using generic filters

Abstract: We will present some old CH constructions due to S. Shelah. As usual they use transfinie induction, diagonalization and enumeration of all relevant objects in type ω1. However, the use of the Martin's axiom type arguments makes them additionally powerful.







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 (Ph.D. student UW)
  • Piotr Koszmider (IM PAN)
  • Wiesław Kubiś (Czech Academy and UKSW)
  • Fulgencio Lopez (IM PAN)
  • Arturo Martínez-Celis (IM PAN)
  • Tomasz Weiss (UKSW)
  • Piotr Zakrzewski (UW)
Forthcoming talks :


  • 22.11 Tomasz Kochanek (MIMUW/IMPAN): On bases in Banach spaces w.r.t. filters and the pseudointersection number p.