19 citations · 120 across the 58 of their papers we have counts for
6 papers · 1 filter
Subsets of Virtually Nilpotent Groups with the SBM Property
Ryan Burkhart, Isaac Goldbring
We extend Leth's notion of subsets of the integers satisfying the Standard interval measure (SIM) property to the class of virtually nilpotent groups and name the corresponding pro…
A nonstandard take on central sets
Isaac Goldbring
We present the basic theory of central subsets of semigroups from the nonstandard perspective. A key feature of this perspective is the replacement of the algebra of ultrafilters w…
On supra-SIM sets of natural numbers
Isaac Goldbring, Steven Leth
We introduce the class of supra-SIM sets of natural numbers. We prove that this class is partition regular and closed under finite-embeddability. We also prove some results on sums…
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…
High density piecewise syndeticity of product sets in amenable groups
Mauro Di Nasso, Isaac Goldbring, Renling Jin +3
M. Beiglböck, V. Bergelson, and A. Fish proved that if is a countable amenable group and and are subsets of with positive Banach density, then the product set …