Ramsey theory without pigeonhole principle and the adversarial Ramsey principle

Noé de Rancourt

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arXiv · 1805.04954

Ramsey theory without pigeonhole principle and the adversarial Ramsey principle

Noé de Rancourt

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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.

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Noé de Rancourt. 2018-05-13. Ramsey theory without pigeonhole principle and the adversarial Ramsey principle. https://arxiv.org/abs/1805.04954

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