Michal Doucha: Canonical Ramsey theory on Polish spaces

Monday, December 9, 2013, 16.30
Seminar room 0.011, Mathematical Institute, University of Bonn

Speaker: Michal Doucha (HIM Bonn)

Title: Canonical Ramsey theory on Polish spaces

Abstract: Canonical Ramsey theory on Polish spaces is a new research area (and book of the same name) initiated by Kanovei Sabok and Zapletal. It generalizes the classical Erdos-Rado canonical Ramsey theorem by considering Polish spaces equipped with sigma-ideals of the Borel algebra and definable equivalence relations on them instead of the set of natural numbers and arbitrary equivalence relations as in the classical case. It has connections to other areas of set theory, e.g. forcing, the theory of Borel equivalence relations, etc. I will give an introduction to this topic and present one of my results in this area (either related to the Silver ideal/forcing, Laver ideal/forcing, or related to the Carlson-Simpson Dual Ramsey theorem).

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