ITERATED HYPER-EXTENSIONS AND AN IDEMPOTENT ULTRAFILTER PROOF OF RADO'S THEOREM

摘要

By using nonstandard analysis, and in particular iterated hyperextensions, 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.