Henkin-Keisler Models

by George Weaver

Overview

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.

Product Details

ISBN-13:	9780792343660
Publisher:	Springer US
Publication date:	01/31/1997
Series:	Mathematics and Its Applications , #392
Edition description:	1997
Pages:	258
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Keisler,s Specialization of the Method of Constants.- The Cardinality of Henkin-Keisler Models.- Classifying Maximal Extensions.- Elementary Subsystems of Henkin-Keisler Models I.- Elementary Subsystems of Henkin-Keisler Models II.- Small Models.- The Keisler-Shelah Isomorphism Theorems.- Saturated Models.

Editorial Reviews

Highlights the little known models that emerged when Keisler modified Henkin's 1949 construction in 1965 at the point where new individual constants are introduced, in order to illuminate a connection between the new models and ultraproducts and prove the Fundamental Theorem of Ultraproducts. Discusses the nature of Keisler's specialization of the method, the cardinality of the new models, classifying maximal extensions, elementary subsystems, small models, isomorphism theorems, and saturated models. Assumes a familiarity with Henkin's proof of the completeness of first order logic and naive set theory. Annotation c. by Book News, Inc., Portland, Or.

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