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.
Citation
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
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