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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 arithmeticLinks
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Citations of this work
Non-principal ultrafilters, program extraction and higher-order reverse mathematics.Alexander P. Kreuzer - 2012 - Journal of Mathematical Logic 12 (1):1250002-.
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.
References found in this work
An effective proof that open sets are Ramsey.Jeremy Avigad - 1998 - Archive for Mathematical Logic 37 (4):235-240.
Hindman’s theorem, ultrafilters, and reverse mathematics.Jeffry L. Hirst - 2004 - Journal of Symbolic Logic 69 (1):65-72.
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