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© 2019

Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory

Benefits

  • 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

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2239)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 3-10
    3. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 11-43
    4. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 45-48
    5. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 49-54
    6. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 55-70
  3. Ramsey Theory

    1. Front Matter
      Pages 71-71
    2. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 73-79
    3. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 81-88
    4. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 89-98
    5. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 99-108
  4. Combinatorial Number Theory

    1. Front Matter
      Pages 109-109
    2. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 111-122
    3. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 123-131
    4. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 133-143
    5. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 145-152
    6. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 153-160
    7. Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 161-169
  5. Other Topics

    1. Front Matter
      Pages 171-171

About this book

Introduction

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.


Keywords

Combinatorial number theory Nonstandard analysis Partition regular Ramsey theory Ultrafilter

Authors and affiliations

  1. 1.Department of MathematicsUniversita di PisaPisaItaly
  2. 2.Department of MathematicsUniversity of California, IrvineIrvineUSA
  3. 3.School of Mathematics and StatisticsVictoria University of WellingtonWellingtonNew Zealand

Bibliographic information

  • Book Title Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory
  • Authors Mauro Di Nasso
    Isaac Goldbring
    Martino Lupini
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lect.Notes Mathematics
  • DOI https://doi.org/10.1007/978-3-030-17956-4
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-030-17955-7
  • eBook ISBN 978-3-030-17956-4
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages XVI, 206
  • Number of Illustrations 2 b/w illustrations, 0 illustrations in colour
  • Topics Combinatorics
    Mathematical Logic and Foundations
  • Buy this book on publisher's site