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Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory - Mauro Di Nasso, Isaac Goldbring, Martino Lupini

Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory

Buch | Softcover
XVI, 206 Seiten
2019 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-17955-7 (ISBN)
CHF 74,85 inkl. MwSt

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.


- 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.

Erscheinungsdatum
Reihe/Serie Lecture Notes in Mathematics
Zusatzinfo XVI, 206 p. 2 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 349 g
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Graphentheorie
Mathematik / Informatik Mathematik Logik / Mengenlehre
Schlagworte combinatorial number theory • combinatorics • nonstandard analysis • Partition regular • Ramsey theory • Ultrafilter
ISBN-10 3-030-17955-9 / 3030179559
ISBN-13 978-3-030-17955-7 / 9783030179557
Zustand Neuware
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