Ramsey theory without pigeonhole principle and the adversarial Ramsey principle
Logic
2020-01-22 v3 Combinatorics
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.
Keywords
Cite
@article{arxiv.1805.04954,
title = {Ramsey theory without pigeonhole principle and the adversarial Ramsey principle},
author = {Noé de Rancourt},
journal= {arXiv preprint arXiv:1805.04954},
year = {2020}
}
Comments
To appear in Trans. Amer. Math. Soc. Peer-reviewed version. 37 pages