Slawomir Solecki : An abstract approach to finite Ramsey theory

Posted by Isaac Goldbring , part of the Logic Seminar.

At

April 9, 2013, 4 p.m.

In

SEO 427

Abstract

I will present an abstract approach to finite Ramsey theory, which reveals the formal algebraic structure underlying results of that theory and which yields most of the results of the theory. I will formulate within this approach an abstract pigeonhole principle and an abstract Ramsey condition, and state a theorem that the pigeonhole principle implies the Ramsey condition. I will illustrate how the general approach is applied on new concrete examples of Ramsey statements---a common generalization of Deuber's and Jasinski's Ramsey statements for trees, the self-dual Ramsey statement, and a Ramsey statement for 1-Lipschitz functions.