4 papers · 1 filter
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…
Translation invariant filters and van der Waerden's Theorem
Mauro Di Nasso
We present a self-contained proof of a strong version of van der Waerden's Theorem. By using translation invariant filters that are maximal with respect to inclusion, a simple indu…
Ramsey properties of nonlinear Diophantine equations
Mauro Di Nasso, Lorenzo Luperi Baglini
We prove general sufficient and necessary conditions for the partition regularity of Diophantine equations, which extend the classic Rado's Theorem by covering large classes of non…
An Elementary Proof of Jin's Theorem with a Bound
Mauro Di Nasso
We present a short proof of Jin's theorem which is entirely elementary, in the sense that no use is made of nonstandard analysis, ergodic theory, measure theory, ultrafilters, or o…