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Henkin-Keisler Models : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - George Weaver

Henkin-Keisler Models

MATHEMATICS AND ITS APPLICATIONS (KLUWER )

Hardcover

Published: December 2009
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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.

Preface
Introductionp. 1
Keisler's Specialization of the Method of Constantsp. 19
The Cardinality of Henkin-Keisler Modelsp. 29
Classifying Maximal Extensionsp. 51
Elementary Subsystems of Henkin-Keisler Models Ip. 61
Elementary Subsystems of Henkin-Keisler Models IIp. 111
Small Modelsp. 129
The Keisler-Shelah Isomorphism Theoremsp. 151
Saturated Modelsp. 199
A Proof of Banach's Theoremp. 239
Index: Symbolsp. 241
Index: Definitionsp. 245
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792343660
ISBN-10: 0792343662
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 258
Published: December 2009
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.77 x 17.15  x 1.91
Weight (kg): 0.64