A lower bound on Gowers' FIN_k theorem
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 ACA$_0$.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2015
- DOI:
- 10.48550/arXiv.1510.01838
- arXiv:
- arXiv:1510.01838
- Bibcode:
- 2015arXiv151001838K
- Keywords:
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- Mathematics - Logic