Description

Book Synopsis
Presents the basic facts about ultrafilters and ultraproducts to readers with no prior knowledge of the subject. These techniques are then applied to a wide variety of topics. The first part of the book deals solely with ultrafilters; the second part presents the classical ultraproduct construction.

Table of Contents
  • Ultrafilters and their applications: Ultrafilter basics
  • Arrow's theorem on fair voting
  • Ultrafilters in topology
  • Ramsey theory and combinatorial number theory
  • Foundational concerns
  • Classical ultraproducts: Classical ultraproducts
  • Applicationis to geometry, commutative algebra, and number theory
  • Ultraproducts and saturation
  • Nonstandard analysis
  • Limit groups
  • Metric ultraproducts and their applications: Metric ultraproducts
  • Asymptotic cones and Gromov's theorem
  • Sofic groups
  • Functional analysis
  • Advanced topics: Does an ultrapower depend on the ultrafilter?
  • The Keisler-Shelah theorem
  • Large cardinals
  • Appendices: Logic
  • Set theory
  • Category theory
  • Hints and solutions to selected exercises
  • Bibliography
  • Index

Ultrafilters Throughout Mathematics

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    £63.90

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    RRP £71.00 – you save £7.10 (10%)

    Order before 4pm today for delivery by Mon 22 Jun 2026.

    A Paperback by Isaac Goldbring

    15 in stock


      View other formats and editions of Ultrafilters Throughout Mathematics by Isaac Goldbring

      Publisher: MP-AMM American Mathematical
      Publication Date: 8/30/2022 12:00:00 AM
      ISBN13: 9781470469610, 978-1470469610
      ISBN10: 1470469618

      Description

      Book Synopsis
      Presents the basic facts about ultrafilters and ultraproducts to readers with no prior knowledge of the subject. These techniques are then applied to a wide variety of topics. The first part of the book deals solely with ultrafilters; the second part presents the classical ultraproduct construction.

      Table of Contents
      • Ultrafilters and their applications: Ultrafilter basics
      • Arrow's theorem on fair voting
      • Ultrafilters in topology
      • Ramsey theory and combinatorial number theory
      • Foundational concerns
      • Classical ultraproducts: Classical ultraproducts
      • Applicationis to geometry, commutative algebra, and number theory
      • Ultraproducts and saturation
      • Nonstandard analysis
      • Limit groups
      • Metric ultraproducts and their applications: Metric ultraproducts
      • Asymptotic cones and Gromov's theorem
      • Sofic groups
      • Functional analysis
      • Advanced topics: Does an ultrapower depend on the ultrafilter?
      • The Keisler-Shelah theorem
      • Large cardinals
      • Appendices: Logic
      • Set theory
      • Category theory
      • Hints and solutions to selected exercises
      • Bibliography
      • Index

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