Combinatorial proofs of Gowers' FIN${}_k$ and FIN${}_k^{\pm }$ theorem

Abstract

A combinatorial proof of a pigeonhole principle of Gowers is found along with its symmetric and approximate version, FIN${}_k^{\pm }$ theorem. The proofs do not use of the concept of ultrafilter.

arXiv commentAn error in Lemma 1

References in corpus (1)

• Finite forms of Gowers' Theorem on the oscillation stability of $c_0$