A lower bound on Gowers' FINk theorem
Abstract
Gowers' FINk 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' FINk theorem does not follow from ACA0.
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