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arXiv · 1304.3009

Iterated hyper-extensions and an idempotent ultrafilter proof of Rado's theorem

Mauro Di Nasso
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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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Mauro Di Nasso. 2013-08-30. Iterated hyper-extensions and an idempotent ultrafilter proof of Rado's theorem. https://arxiv.org/abs/1304.3009

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