19 citations · 47 across the 12 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…
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…