Nonstandard methods in Ramsey theory and combinatorial number theory / Mauro Di Nasso, Isaac Goldbring, Martino Lupini.
Di Nasso, Mauro, 1963- author.; Goldbring, Isaac, author.; Lupini, Martino, author.
2019
QA166 .D5 2019
Available Online

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Title Nonstandard methods in Ramsey theory and combinatorial number theory / Mauro Di Nasso, Isaac Goldbring, Martino Lupini.
Author Di Nasso, Mauro, 1963- author.
ISBN 9783030179564 (electronic book)
3030179567 (electronic book)
3030179559
9783030179557
DOI https://doi.org/10.1007/978-3-030-17
Published Cham, Switzerland : Springer, [2019]
Language English
Description 1 online resource (xvi, 206 pages) : illustrations.
Item Number 10.1007/978-3-030-17 doi
Call Number QA166 .D5 2019
Dewey Decimal Classification 511.6
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on online resource; title from digital title page (viewed on June 25, 2019).
Added Author Goldbring, Isaac, author.
Lupini, Martino, author.
Series Lecture notes in mathematics (Springer-Verlag) ; 2239.
Available in Other Form Print version 9783030179557
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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.

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