Iterated hyper-extensions and an idempotent ultrafilter proof of Rado’s Theorem

Di Nasso, Mauro

doi:10.1090/S0002-9939-2014-12342-2

Iterated hyper-extensions and an idempotent ultrafilter proof of Rado’s Theorem
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Proc. Amer. Math. Soc. 143 (2015), 1749-1761 Request permission

Abstract:

By using nonstandard analysis, and in particular iterated hyper-extensions, we give foundations to a peculiar way of manipulating ultrafilters on the natural numbers and their pseudo-sums. The resulting formalism is suitable for applications in Ramsey theory of numbers. To illustrate the use of our technique, we give a (rather) short proof of Milliken-Taylor’s Theorem and a ultrafilter version of Rado’s Theorem about partition regularity of diophantine equations.

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