A lower bound on Gowers' FIN_k theorem

2015/10/07 by Alexander P. Kreuzer, Kreuzer, Alexander P.
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.1510.01838

arxiv created 2015/10/07 · arxiv updated 2015/10/08

Abstract

Gowers' FIN_k theorem, also called Gowers' pigeonhole principle or Gowers' theorem, is a Ramsey-type theorem. It first occurred in the study of Banach space theory and is a natural generalization of Hindman's theorem. In this short note, we will show that Gowers' FIN_k theorem does not follow from ACA₀.

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