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Henkin-Keisler Models

  • Book
  • © 1997

Overview

Authors:
  1. George Weaver

    1. Bryn Mawr College, USA

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Part of the book series: Mathematics and Its Applications (MAIA, volume 392)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    Pages 1-17

  3. Keisler,s Specialization of the Method of Constants

    Pages 19-27

  4. The Cardinality of Henkin-Keisler Models

    Pages 29-50

  5. Classifying Maximal Extensions

    Pages 51-60

  6. Elementary Subsystems of Henkin-Keisler Models I

    Pages 61-109

  7. Elementary Subsystems of Henkin-Keisler Models II

    Pages 111-128

  8. Small Models

    Pages 129-149

  9. The Keisler-Shelah Isomorphism Theorems

    Pages 151-197

  10. Saturated Models

    Pages 199-238

  11. Back Matter

    Pages 239-244
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Keywords

About this book

Henkin-Keisler models emanate from a modification of the Henkin construction introduced by Keisler to motivate the definition of ultraproducts. Keisler modified the Henkin construction at that point at which `new' individual constants are introduced and did so in a way that illuminates a connection between Henkin-Keisler models and ultraproducts. The resulting construction can be viewed both as a specialization of the Henkin construction and as an alternative to the ultraproduct construction. These aspects of the Henkin-Keisler construction are utilized here to present a perspective on ultraproducts and their applications accessible to the reader familiar with Henkin's proof of the completeness of first order logic and naive set theory. This approach culminates in proofs of various forms of the Keisler-Shelah characterizations of elementary equivalence and elementary classes via Henkin-Keisler models. The presentation is self-contained and proofs of more advanced results from set theory are introduced as needed.
Audience: Logicians in philosophy, computer science, linguistics and mathematics.

Authors and Affiliations

  • Bryn Mawr College, USA

    George Weaver

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