Submission date: 14 January 2019

Abstract:

We use the model theoretic notion of coheir to give short proofs of old and new theorems in Ramsey Theory. As an illustration we start from Ramsey's theorem itself. Then we prove Hindman's theorem and the Hales-Jewett theorem. Finally, we prove two Ramsey theoretic principles that have among their consequences partition theorems of Carlson and of Gowers.

Mathematics Subject Classification: 05D10 (Primary), 03C98, 03H99 (Secondary)

Keywords and phrases:

Full text arXiv 1901.04363: pdf, ps.