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AuthorWeaver, George. author
TitleHenkin-Keisler Models [electronic resource] / by George Weaver
ImprintBoston, MA : Springer US, 1997
Connect tohttp://dx.doi.org/10.1007/b102616
Descript XII, 258 p. online resource

SUMMARY

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 ǹew' 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


CONTENT

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


Mathematics Logic Computer science Mathematical logic Mathematics Mathematical Logic and Foundations Logic Computer Science general



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