Model Theory

Third Edition

By: C.C. CHANG

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Paperback | 13 June 2012 | Edition Number 3

At a Glance

Paperback
672 Pages

Edition Type
Revised

Grade
17+

Dimensions(cm)
23.5 x 15.5 x 3.3

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Model theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. This is the first and most successful textbook in logical model theory. Extensively updated and corrected in 1990 to accommodate developments in model theoretic methods - including classification theory and nonstandard analysis - the third edition added entirely new sections, exercises, and references. Each chapter introduces an individual method and discusses specific applications. Basic methods of constructing models include constants, elementary chains, Skolem functions, indiscernibles, ultraproducts, and special models. The final chapters present more advanced topics that feature a combination of several methods. This classic treatment covers most aspects of first-order model theory and many of its applications to algebra and set theory.

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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Mathematical Logic Set Theory Science Science in General

Introduction	p. 1
What is model theory?	p. 1
Model theory for sentential logic	p. 4
Languages, models and satisfaction	p. 18
Theories and examples of theories	p. 36
Elimination of quantifiers	p. 49
Models constructed from constants	p. 61
Completeness and compactness	p. 61
Refinements of the method. Omitting types and interpolation theorems	p. 77
Countable models of complete theories	p. 96
Recursively saturated models	p. 109
Lindstrom's characterization of first order logic	p. 127
Further model-theoretic constructions	p. 136
Elementary extensions and elementary chains	p. 136
Applications of elementary chains	p. 147
Skolem functions and indiscernibles	p. 163
Some examples	p. 178
Model completeness	p. 186
Ultraproducts	p. 211
The fundamental theorem	p. 211
Measurable cardinals	p. 227
Regular ultrapowers	p. 248
Nonstandard universes	p. 262
Saturated and special models	p. 292
Saturated and special models	p. 292
Preservation theorems	p. 306
Applications of special models to the theory of definability	p. 323
Applications to field theory	p. 342
Application to Boolean algebras	p. 372
More about ultraproducts and generalizations	p. 384
Ultraproducts which are saturated	p. 384
Direct products, reduced products, and Horn sentences	p. 405
Direct products, reduced products, and Horn sentences (continued)	p. 420
Limit ultrapowers and complete extensions	p. 447
Iterated ultrapowers	p. 453
Selected topics	p. 482
Categoricity in power	p. 482
An extension of Ramsey's theorem and applications; some two-cardinal theorems	p. 509
Models of large cardinality	p. 534
Large cardinals and the constructible universe	p. 558
Set theory	p. 579
Open problems in classical model theory	p. 597
Historical notes	p. 603
References	p. 623
Additional references	p. 634
Index of definitions	p. 641
Index of symbols	p. 649
Table of Contents provided by Ingram. All Rights Reserved.

Model Theory

Third Edition

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

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