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March 2004 Hindman’s theorem, ultrafilters, and reverse mathematics
Jeffry L. Hirst
J. Symbolic Logic 69(1): 65-72 (March 2004). DOI: 10.2178/jsl/1080938825

Abstract

Assuming 𝖢𝖧, Hindman [ht1] showed that the existence of certain ultrafilters on the power set of the natural numbers is equivalent to Hindman’s Theorem. Adapting this work to a countable setting formalized in RCA0, this article proves the equivalence of the existence of certain ultrafilters on countable Boolean algebras and an iterated form of Hindman’s Theorem, which is closely related to Milliken’s Theorem. A computable restriction of Hindman’s Theorem follows as a corollary.

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Jeffry L. Hirst. "Hindman’s theorem, ultrafilters, and reverse mathematics." J. Symbolic Logic 69 (1) 65 - 72, March 2004. https://doi.org/10.2178/jsl/1080938825

Information

Published: March 2004
First available in Project Euclid: 2 April 2004

zbMATH: 1070.03039
MathSciNet: MR2039345
Digital Object Identifier: 10.2178/jsl/1080938825

Subjects:
Primary: 03B30 , 03D80 , 03F35 , 05D10

Keywords: computability , Hindman’s Theorem , Milliken’s Theorem , reverse mathematics

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 1 • March 2004
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