Ramsey theory without pigeonhole principle and the adversarial Ramsey principle

Abstract

We develop a general framework for infinite-dimensional Ramsey theory with and without pigeonhole principle, inspired by Gowers' Ramsey-type theorem for block sequences in Banach spaces and by its exact version proved by Rosendal. In this framework, we prove the adversarial Ramsey principle for Borel sets, a result conjectured by Rosendal that generalizes at the same time his version of Gowers' theorem and Borel determinacy of games on integers.

arXiv commentTo appear in Trans. Amer. Math. Soc. Peer-reviewed version. 37 pages

Cited by in corpus (2)

• Local Banach-space dichotomies and ergodic spaces
• Filters on a countable vector space