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The Theory of Ultrafilters

  • Book
  • © 1974

Overview

Authors:
  1. W. Wistar Comfort

    1. Department of Mathematics, Wesleyan University, Middletown, USA

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  2. Stylianos Negrepontis

    1. Department of Mathematics, Athens University, Athens, Greece
      Department of Mathematics, McGill University, Montréal, Canada

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 211)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-X
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  2. Set Theory

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 1-20

  3. Topology and Boolean Algebras

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 21-60

  4. Intersection Systems and Families of Large Oscillation

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 61-81

  5. The General Theory of Jónsson Classes

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 82-100

  6. The Jónsson Class of Ordered Sets

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 101-115

  7. The Jónsson Class of Boolean Algebras

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 116-141

  8. Basic Facts on Ultrafilters

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 142-163

  9. Large Cardinals

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 164-203

  10. The Rudin-Keisler Order on Types of Ultrafilters

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 204-232

  11. Good Ultrafilters

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 233-261

  12. Elementary Types

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 262-285

  13. Families of Almost Disjoint Sets

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 286-310

  14. Saturation of Ultraproducts

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 311-340

  15. Topology of Spaces of Ultrafilters

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 341-380

  16. Spaces Homeomorphic to (2α) α

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 381-409

  17. Ultrafilters on ω

    • W. Wistar Comfort, Stylianos Negrepontis
    Pages 410-452

  18. Back Matter

    Pages 453-484
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Keywords

About this book

An ultrafilter is a truth-value assignment to the family of subsets of a set, and a method of convergence to infinity. From the first (logical) property arises its connection with two-valued logic and model theory; from the second (convergence) property arises its connection with topology and set theory. Both these descriptions of an ultrafilter are connected with compactness. The model-theoretic property finds its expression in the construction of the ultraproduct and the compactness type of theorem of Los (implying the compactness theorem of first-order logic); and the convergence property leads to the process of completion by the adjunction of an ideal element for every ultrafilter-i. e. , to the Stone-Cech com­ pactification process (implying the Tychonoff theorem on the compact­ ness of products). Since these are two ways of describing the same mathematical object, it is reasonable to expect that a study of ultrafilters from these points of view will yield results and methods which can be fruitfully crossbred. This unifying aspect is indeed what we have attempted to emphasize in the present work.

Authors and Affiliations

  • Department of Mathematics, Wesleyan University, Middletown, USA

    W. Wistar Comfort

  • Department of Mathematics, Athens University, Athens, Greece

    Stylianos Negrepontis

  • Department of Mathematics, McGill University, Montréal, Canada

    Stylianos Negrepontis

Bibliographic Information

  • Book Title: The Theory of Ultrafilters

  • Authors: W. Wistar Comfort, Stylianos Negrepontis

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-65780-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin · Heidelberg 1974

  • Softcover ISBN: 978-3-642-65782-5Published: 12 November 2011

  • eBook ISBN: 978-3-642-65780-1Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: X, 484

  • Topics: Topology

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