Abstract
W. T. Gowers' c 0 theorem asserts that for every Lipschitz function F : S c0 → R and e > 0, there exists an infinite-dimensional subspace Y of c 0 such that the oscillation of F on Sy is at most e. The proof of this theorem has been reduced by W. T. Cowers to the proof of a new Ramsey type theorem. Our aim is to present a proof of the last result.
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