7 papers
Hypernatural numbers in arithmetic Ramsey theory
Mauro Di Nasso
The hypernatural numbers of nonstandard analysis have recently proven to be an effective tool in arithmetic Ramsey theory. After introducing the fundamental ``nonstand…
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…
Monochromatic sums and quotients in
Mauro Di Nasso, Lorenzo Luperi Baglini, Rosario Mennuni +2
We prove partition regularity of the configuration in a strong infinitary form that extends Hindman's Theorem. We study the related issue of partition regularity of c…
A new ultrafilter proof of Van der Waerden's theorem
Mauro Di Nasso
We present a new short proof of Van der Waerden's Theorem about the existence of arbitrarily long monochromatic arithmetic progressions. The proof uses algebra in the compact space…
Ramsey's witnesses
Mauro Di Nasso, Lorenzo Luperi Baglini, Marcello Mamino +2
We introduce the notion of Ramsey partition regularity, a generalisation of partition regularity involving infinitary configurations. We provide characterisations of this notion in…
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…