Ramsey theory without pigeonhole principle and the adversarial Ramsey principle
Copyright policy )Ramsey theory without pigeonhole principle and the adversarial Ramsey principle
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.
- PSL Research University France
- Sorbonne Paris Cité France
- University of Vienna Austria
- Paris Diderot University France
- Institut de Mathématiques de Jussieu France
Infinite-dimensional Ramsey theory, Determinacy principles, Isomorphic theory (including renorming) of Banach spaces, Cowers' games, Gowers' games, 101013 Mathematische Logik, Gowers’ games, Ramsey theory, DETERMINACY, infinite-dimensional Ramsey theory, Mathematics - Logic, 05D10, 03E60, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], 101013 Mathematical logic, Determinacy, FOS: Mathematics, [MATH.MATH-LO] Mathematics [math]/Logic [math.LO], Mathematics - Combinatorics, Combinatorics (math.CO), determinacy, Logic (math.LO)
Infinite-dimensional Ramsey theory, Determinacy principles, Isomorphic theory (including renorming) of Banach spaces, Cowers' games, Gowers' games, 101013 Mathematische Logik, Gowers’ games, Ramsey theory, DETERMINACY, infinite-dimensional Ramsey theory, Mathematics - Logic, 05D10, 03E60, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], 101013 Mathematical logic, Determinacy, FOS: Mathematics, [MATH.MATH-LO] Mathematics [math]/Logic [math.LO], Mathematics - Combinatorics, Combinatorics (math.CO), determinacy, Logic (math.LO)
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