19 citations · 47 across the 12 of their papers we have counts for
12 papers
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…
Self-divisible ultrafilters and congruences in
Mauro Di Nasso, Lorenzo Luperi Baglini, Rosario Mennuni +2
We introduce self-divisible ultrafilters, which we prove to be precisely those such that the weak congruence relation introduced by Šobot is an equivalence relation…
Euclidean integers, Euclidean ultrafilters, and Euclidean numerosities
Mauro Di Nasso, Marco Forti
We introduce axiomatically the ring of the Euclidean integers, that can be viewed as the ``integral part" of the field of Euclidean numbers of [4], where th…
Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory
Mauro Di Nasso, Isaac Goldbring, Martino Lupini
The goal of this present manuscript is to introduce the reader to the nonstandard method and to provide an overview of its most prominent applications in Ramsey theory and combinat…
Idempotent ultrafilters without Zorn's Lemma
Mauro Di Nasso, Eleftherios Tachtsis
We introduce the notion of additive filter and present a new proof of the existence of idempotent ultrafilters on N without any use of Zorn's Lemma, and where one only assumes the…
Approximate polynomial structure in additively large sets
Mauro Di Nasso, Isaac Goldbring, Renling Jin +3
We show that any subset of the natural numbers with positive logarithmic Banach density contains a set that is within a factor of two of a geometric progression, improving the boun…
Finite Embeddability of Sets and Ultrafilters
Andreas Blass, Mauro Di Nasso
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddabi…
High density piecewise syndeticity of sumsets
Mauro Di Nasso, Isaac Goldbring, Renling Jin +3
Renling Jin proved that if A and B are two subsets of the natural numbers with positive Banach density, then A+B is piecewise syndetic. In this paper, we prove that, under various…
On a sumset conjecture of Erdős
Mauro Di Nasso, Isaac Goldbring, Renling Jin +3
Erdős conjectured that for any set with positive lower asymptotic density, there are infinite sets such that . We…
Nonstandard Analysis and the sumset phenomenon in arbitrary amenable groups
Mauro Di Nasso, Martino Lupini
Beiglboeck, Bergelson and Fish proved that if subsets A,B of a countable discrete amenable group G have positive Banach densities a and b respectively, then the product set AB is p…
Embeddability Properties of Difference Sets
Mauro Di Nasso
By using nonstandard analysis, we prove embeddability properties of difference sets of sets of integers. (A set is "embeddable" into if every finite configuration of…
Quasi-selective ultrafilters and asymptotic numerosities
Andreas Blass, Mauro Di Nasso, Marco Forti
We isolate a new class of ultrafilters on N, called "quasi-selective" because they are intermediate between selective ultrafilters and P-points. (Under the Continuum Hypothesis the…