Iterated hyper-extensions and an idempotent ultrafilter proof of Rado's theorem
Logic
2013-09-02 v2
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.
Keywords
Cite
@article{arxiv.1304.3009,
title = {Iterated hyper-extensions and an idempotent ultrafilter proof of Rado's theorem},
author = {Mauro Di Nasso},
journal= {arXiv preprint arXiv:1304.3009},
year = {2013}
}
Comments
Corrected typos