Henkin-Keisler Models
Henkin-Keisler Models by George Weaver is a scholarly work published by Springer US on March 8, 2013. This softcover reprint of the original 1st edition from 1997 spans 258 pages and is presented in English. The book explores the Henkin-Keisler models, which arise from a modification of the Henkin construction introduced by Keisler, focusing on the definition of ultraproducts and their connections to both Henkin constructions and ultraproduct constructions.
Readers will find a detailed examination of the Henkin-Keisler construction, which serves as a foundation for understanding ultraproducts and their applications. The text is designed for those familiar with Henkin’s proof of the completeness of first-order logic and naive set theory, culminating in proofs related to the Keisler-Shelah characterizations of elementary equivalence and elementary classes. The presentation is self-contained, with advanced results from set theory introduced as necessary, making it a valuable resource for logicians in fields such as philosophy, computer science, linguistics, and mathematics.
Official synopsis Publisher
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.
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