Models And Ultraproducts
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Models And Ultraproducts
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Author : John Lane Bell
language : en
Publisher: Courier Corporation
Release Date : 2006-01-01
Models And Ultraproducts written by John Lane Bell and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Mathematics categories.
In this text for first-year graduate students, the authors provide an elementary exposition of some of the basic concepts of model theory--focusing particularly on the ultraproduct construction and the areas in which it is most useful. The book, which assumes only that its readers are acquainted with the rudiments of set theory, starts by developing the notions of Boolean algebra, propositional calculus, and predicate calculus. Model theory proper begins in the fourth chapter, followed by an introduction to ultraproduct construction, which includes a detailed look at its theoretic properties. An overview of elementary equivalence provides algebraic descriptions of the elementary classes. Discussions of completeness follow, along with surveys of the work of Jónsson and of Morley and Vaught on homogeneous universal models, and the results of Keisler in connection with the notion of a saturated structure. Additional topics include classical results of Gödel and Skolem, and extensions of classical first-order logic in terms of generalized quantifiers and infinitary languages. Numerous exercises appear throughout the text.
Models And Ultraproducts
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Author : John Lane Bell
language : en
Publisher:
Release Date : 1971
Models And Ultraproducts written by John Lane Bell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Model theory categories.
Models And Ultraproducts
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Author : John Lane Bell
language : en
Publisher:
Release Date : 1971
Models And Ultraproducts written by John Lane Bell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
The aim of this book is to provide an elementary exposition of some of the basic concepts of model theory. Model theory, which can be described briefly as the study of the relationship between formal languages and abstract structures, covers a very wide field and it is not possible to compress it into one volume. We have chosen as our theme the ultraproducts construction. We hope this book we be of use to undergraduate and practicing mathematicians.
Ultraproducts In The Theory Of Models
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Author : Simon Bernard Kochen
language : en
Publisher:
Release Date : 1961
Ultraproducts In The Theory Of Models written by Simon Bernard Kochen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with categories.
Ultraproducts And Higher Order Models
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Author : Wilfred Gordon Malcolm
language : en
Publisher:
Release Date : 1972
Ultraproducts And Higher Order Models written by Wilfred Gordon Malcolm and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Logic, Symbolic and mathematical categories.
Models And Ultraproducts
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Author : A. B. Slomson
language : en
Publisher: Dover Publications
Release Date : 2013-12-20
Models And Ultraproducts written by A. B. Slomson and has been published by Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with categories.
This first-year graduate text assumes only an acquaintance with set theory to explore homogeneous universal models, saturated structure, extensions of classical first-order logic, and other topics. 1974 edition.
Ultraproducts And Continuous Families Of Models
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Author : Francisco Marmolejo
language : en
Publisher:
Release Date : 1995
Ultraproducts And Continuous Families Of Models written by Francisco Marmolejo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Ultraproducts And Their Application To Model Theory
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Author : Joan Nancy Becker
language : en
Publisher:
Release Date : 1969
Ultraproducts And Their Application To Model Theory written by Joan Nancy Becker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
Henkin Keisler Models
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Author : George Weaver
language : en
Publisher: Springer
Release Date : 2007-07-23
Henkin Keisler Models written by George Weaver and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-23 with Mathematics categories.
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.
Ultraproducts And Elementary Classes
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Author : H. Jerome Keisler
language : en
Publisher:
Release Date : 1961
Ultraproducts And Elementary Classes written by H. Jerome Keisler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Logic, Symbolic and mathematical categories.