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Henkin-Keisler Models (Mathematics and Its Applications)

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Henkin-Keisler Models

Mathematics and Its Applications

By George Weaver

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Format: Paperback, 258 pages, Softcover reprint of Edition
Other Information: biography
Published In: United States, 01 March 2013
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.

Table of Contents

Preface. 1. Introduction. 2. Keisler's Specialization of the Method of Constants. 3. The Cardinality of Henkin-Keisler Models. 4. Classifying Maximal Extensions. 5. Elementary Subsystems of Henkin-Keisler Models I. 6. Elementary Subsystems of Henkin-Keisler Models II. 7. Small Models. 8. The Keisler-Shelah Isomorphism Theorems. 9. Saturated Models. Appendix. Index.

Promotional Information

Springer Book Archives

EAN: 9781475770766
ISBN: 1475770766
Publisher: Springer
Dimensions: 23.5 x 15.5 x 1.5 centimetres (0.39 kg)
Age Range: 15+ years
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