4 papers · 1 filter
A simultaneous extension of Ramsey, Hindman, and Hales-Jewett Theorems
Mauro Di Nasso, Renling Jin
We prove a multidimensional extension of a strong Hales-Jewett theorem that simultaneously and "directly" extends Ramsey's theorem and Hindman's theorem. The proofs show the effect…
A Van der Waerden-free proof of Rado's theorem
Mauro Di Nasso, Lorenzo Luperi Baglini
We present a proof of the sufficiency of Rado's condition for the partition regularity of linear Diophantine equations that avoids any use of van der Waerden's theorem. The proof i…
The magic of tensor products of ultrafilters
Mauro Di Nasso
Tensor products of ultrafilters have special combinatorial features closely related to Ramsey's Theorem, making them useful tools in applications. Here we first review their fundam…
Foundations of iterated star maps and their use in combinatorics
Mauro Di Nasso, Renling Jin
We develop a framework for nonstandard analysis that gives foundations to the interplay between external and internal iterations of the star map, and we present a few examples to s…