# Nonstandard methods in combinatorial number theory

@inproceedings{Nasso2017NonstandardMI, title={Nonstandard methods in combinatorial number theory}, author={Mauro Di Nasso and Isaac Goldbring}, year={2017} }

The purpose of this workshop was to continue the use of nonstandard methods in combinatorial number theory and Ramsey theory. The organizers invited experts in nonstandard analysis, additive combinatorics, Ramsey theory, ergodic theory, and model theory with the hopes that this unique blend of experts would be able to influence each other in a positive way. Every morning there were two lectures addressed to the entire workshop. Due to the afoementioned blend of fields of expertise, the…

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## References

SHOWING 1-10 OF 36 REFERENCES

Building Models by Games

- Mathematics
- 1985

A general method for building infinite mathematical structures, and its applications in algebra and model theory are introduced, and a wide variety of algebraic applications are studied.

Nonstandard analysis for the working mathematician

- Mathematics
- 2000

Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a…

Stable group theory and approximate subgroups

- Mathematics
- 2009

We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group G, we show that a finite…

The structure of approximate groups

- Mathematics
- 2011

Let K⩾1 be a parameter. A K-approximate group is a finite set A in a (local) group which contains the identity, is symmetric, and such that A⋅A is covered by K left translates of A.The main result of…

RANDOMIZATIONS OF MODELS AS METRIC STRUCTURES

- Mathematics
- 2009

The notion of a randomization of a rst order structure was introduced by Keisler in the paper Randomizations of Models, Advances in Math. 1999. The idea was to form a new structure whose elements are…

CLASSIFICATION OF INJECTIVE FACTORS

- Mathematics
- 1981

The fundamental results of A. Connes which determine a complete set of isomorphism classes for most injectlve factors are discussed in detail. After some introductory remarks which lay the foundation…

Definable sets containing productsets in expansions of groups

- MathematicsJournal of Group Theory
- 2019

Abstract We consider the question of when sets definable in first-order expansions of groups contain the product of two infinite sets (we refer to this as the “productset property”). We first show…

Omitting types in operator systems

- Mathematics
- 2015

We show that the class of 1-exact operator systems is not uniformly definable by a sequence of types. We use this fact to show that there is no finitary version of Arveson's extension theorem. Next,…

HIGH DENSITY PIECEWISE SYNDETICITY OF PRODUCT SETS IN AMENABLE GROUPS

- MathematicsThe Journal of Symbolic Logic
- 2016

A quantitative version of the aforementioned result is proved by providing a lower bound on the density (with respect to a Følner sequence) of the set of witnesses to the thickness of EAB by the current set of authors using completely different techniques.