Nonstandard Methods In Ramsey Theory And Combinatorial Number Theory by Mauro Di NassoNonstandard Methods In Ramsey Theory And Combinatorial Number Theory by Mauro Di Nasso

Nonstandard Methods In Ramsey Theory And Combinatorial Number Theory

byMauro Di Nasso, Isaac Goldbring, Martino Lupini

Paperback | May 24, 2019

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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.


Title:Nonstandard Methods In Ramsey Theory And Combinatorial Number TheoryFormat:PaperbackDimensions:206 pagesPublished:May 24, 2019Publisher:Springer NatureLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3030179559

ISBN - 13:9783030179557

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Table of Contents

-Part I Preliminaries. - Ultrafilters. - Nonstandard Analysis. - Hyperfinite Generators of Ultrafilters. - Many Stars: Iterated Nonstandard Extensions. - LoebMeasure. - Part II Ramsey Theory. - Ramsey's Theorem. - The Theorems of van der Waerden and Hales-Jewett. - From Hindman to Gowers. - Partition Regularity of Equations. - Part III Combinatorial Number Theory . - Densities and Structural Properties. - Working in the Remote Realm. - Jin's Sumset Theorem. - Sumset Configurations in Sets of Positive Density. - Near Arithmetic Progressions in Sparse Sets. - The Interval Measure Property. - Part IV Other Topics. - Triangle Removal and Szemerédi Regularity. - Approximate Groups. - Foundations of Nonstandard Analysis.