5 papers
Abstract densities and ideals of sets
Mauro Di Nasso, Renling Jin
Abstract upper densities are monotone and subadditive functions from the power set of positive integers to the unit real interval that generalize the upper densities used in number…
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…
Fermat-like equations that are not partition regular
Mauro Di Nasso, Maria Riggio
By means of elementary conditions on coefficients, we isolate a large class of Fermat-like Diophantine equations that are not partition regular, the simplest examples being $x^n+y^…
Elementary numerosity and measures
Vieri Benci, Emanuele Bottazzi, Mauro Di Nasso
In this paper we introduce the notion of elementary numerosity as a special function defined on all subsets of a given set X which takes values in a suitable non-Archimedean field,…
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…