2018/05/13 by Noé de Rancourt, de Rancourt, Noé
Mathematics · #Advanced Topology and Set Theory #Advanced Banach Space Theory #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.1805.04954
We develop a general framework for infinite-dimensional Ramsey theory with\nand without pigeonhole principle, inspired by Gowers' Ramsey-type theorem for\nblock sequences in Banach spaces and by its exact version proved by Rosendal.\nIn this framework, we prove the adversarial Ramsey principle for Borel sets, a\nresult conjectured by Rosendal that generalizes at the same time his version of\nGowers' theorem and Borel determinacy of games on integers.\n