MATH 7820: Seminar in Logic (Spring 2012)

Instructor: Richard Shore

As usual, the logic seminar will have one meeting a week devoted to a specific topic and the other used for people speaking on their own work or interests as well as outside speakers.

I am proposing as the topic for this semester the study of Ramsey type theorems from the viewpoints of computability and reverse mathematics. At the lower end in terms of computational complexity and proof theoretic strength, we will consider the classical Ramsey Theorem and various combinatorial consequences (such as chain-antichain in p.o. and chains in linear orders) that are provably weaker than the basic theorems. At the higher ends, we should look at theorems such as Hindman’s, Auslander-Ellis, the open (and more) Ramsey theorem and the dual Ramsey theorem as time permits.

Comments on and suggestions for the topic choice (both pro and alternative) are welcome.