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HenkinKeisler 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 HenkinKeisler 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 HenkinKeisler 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 KeislerShelah characterizations of elementary equivalence and elementary classes via HenkinKeisler models. The presentation is selfcontained 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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This product may contain chemicals known to the State of California to cause cancer,
birth defects, or other reproductive harm.
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