impan seminar:

working group in applications of set theory



UNUSUAL TIME AND PLACE: 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.

Previous talks this semester:








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)
  • Piotr Koszmider (IM PAN)
  • Fulgencio Lopez (IM PAN)
  • Arturo Martínez-Celis (IM PAN)
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.