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