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Hindman's theorem, ultrafilters, and reverse mathematics
Published online by Cambridge University Press: 12 March 2014
Abstract
Assuming CH. Hindman [2] 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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- Copyright © Association for Symbolic Logic 2004
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