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Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory

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Cover of 'Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory'

Table of Contents

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    Book Overview
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    Chapter 1 Ultrafilters
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    Chapter 2 Nonstandard Analysis
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    Chapter 3 Hyperfinite Generators of Ultrafilters
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    Chapter 4 Many Stars: Iterated Nonstandard Extensions
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    Chapter 5 Loeb Measure
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    Chapter 6 Ramsey’s Theorem
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    Chapter 7 The Theorems of van der Waerden and Hales-Jewett
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    Chapter 8 From Hindman to Gowers
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    Chapter 9 Partition Regularity of Equations
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    Chapter 10 Densities and Structural Properties
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    Chapter 11 Working in the Remote Realm
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    Chapter 12 Jin’s Sumset Theorem
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    Chapter 13 Sumset Configurations in Sets of Positive Density
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    Chapter 14 Near Arithmetic Progressions in Sparse Sets
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    Chapter 15 The Interval Measure Property
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    Chapter 16 Triangle Removal and Szemerédi Regularity
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    Chapter 17 Approximate Groups
Attention for Chapter 14: Near Arithmetic Progressions in Sparse Sets
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