TY - BOOK ID - 17528863 TI - Henkin-Keisler models PY - 1997 SN - 0792343662 0585288445 PB - Dordrecht ; Boston ; London : Kluwer Academic Publishers, DB - UniCat KW - Ultraproducts KW - First-order logic KW - Mathematics. KW - Logic. KW - Computer science. KW - Mathematical logic. KW - Mathematical Logic and Foundations. KW - Computer Science, general. KW - Logic, Symbolic and mathematical. KW - Model theory KW - Prime products KW - Products, Prime KW - Products, Ultra KW - -Ultra-products KW - Logic, Symbolic and mathematical KW - Logic, Modern KW - Informatics KW - Science KW - Argumentation KW - Deduction (Logic) KW - Deductive logic KW - Dialectic (Logic) KW - Logic, Deductive KW - Intellect KW - Philosophy KW - Psychology KW - Reasoning KW - Thought and thinking KW - Algebra of logic KW - Logic, Universal KW - Mathematical logic KW - Symbolic and mathematical logic KW - Symbolic logic KW - Mathematics KW - Algebra, Abstract KW - Metamathematics KW - Set theory KW - Syllogism KW - Methodology KW - Model theory. KW - First-order logic. UR - https://www.unicat.be/uniCat?func=search&query=sysid:17528863 AB - 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. ER -