Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory, 1st ed. 2019 Lecture Notes in Mathematics Series, Vol. 2239

The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.

Presents the first introduction to nonstandard methods geared towards combinatorics

Includes new nonstandard proofs of classical results in Ramsey theory

Provides a self-contained introduction to the literature of nonstandard methods in combinatorics

Numerous exercises help readers to familiarize themselves with the material