19 citations · 120 across the 58 of their papers we have counts for
6 papers · 1 filter
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…
Existentially closed II_1 factors
Ilijas Farah, Isaac Goldbring, Bradd Hart +1
We examine the properties of existentially closed (R^omega-embeddable) II_1 factors. In particular, we use the fact that every automorphism of an existentially closed (R^omega-embe…
A computability-theoretic reformulation of the Connes Embedding Problem
Isaac Goldbring, Bradd Hart
The Connes Embedding Problem (CEP) asks whether every separable II_1 factor embeds into an ultrapower of the hyperfinite II_1 factor. We show that the CEP is equivalent to the comp…
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…
Definable closure in randomizations
Uri Andrews, Isaac Goldbring, H. Jerome Keisler
The randomization of a complete first order theory T is the complete continuous theory T^R with two sorts, a sort for random elements of models of T, and a sort for events in an un…
Amalgamating R^ω-embeddable von Neumann algebras
Ilijas Farah, Isaac Goldbring, Bradd Hart
We observe how a classical model-theoretic fact proves the existence of many strong amalgamation bases for the class of R^ω-embeddable von Neumann algebras, where R is the hyperfin…