Hindman's theorem: An ultrafilter argument in second order arithmetic

Journal of Symbolic Logic 76 (1):353 - 360 (2011)

Abstract
Hindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated into second order arithmetic
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DOI 10.2178/jsl/1294171005
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An Effective Proof That Open Sets Are Ramsey.Jeremy Avigad - 1998 - Archive for Mathematical Logic 37 (4):235-240.

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Ultrafilters in Reverse Mathematics.Henry Towsner - 2014 - Journal of Mathematical Logic 14 (1):1450001.
A Simple Proof and Some Difficult Examples for Hindman's Theorem.Henry Towsner - 2012 - Notre Dame Journal of Formal Logic 53 (1):53-65.

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