3 papers
math.NT2026
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 ``nons…
math.LO2026
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…
math.CO2022
Central sets and infinite monochromatic exponential patterns
Mauro Di Nasso, Mariaclara Ragosta
A cornerstone of Arithmetic Ramsey Theory is \emph{Hindman's Theorem} of 1974: "For every finite coloring of the natural numbers, there exists an infinite sequence such tha…