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Model theory

Author: Wilfrid Hodges
Publisher: Cambridge [England] ; New York : Cambridge University Press, 1993.
Series: Encyclopedia of mathematics and its applications, v. 42.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"This is an up-to-date and integrated introduction to model theory, designed to be used for graduate courses (for students who are familiar with first-order logic), and as a reference for more experienced logicians and mathematicians." "Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide variety of other areas such as set theory,  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Wilfrid Hodges
ISBN: 0521304423 9780521304429 9780521066365 0521066360
OCLC Number: 24173886
Description: xiii, 772 pages : illustrations ; 24 cm.
Contents: 1. Naming of parts. 1.1. Structures. 1.2. Homomorphisms and substructures. 1.3. Terms and atomic formulas. 1.4. Parameters and diagrams. 1.5. Canonical models --
2. Classifying structures. 2.1. Definable subsets. 2.2. Definable classes of structures. 2.3. Some notions from logic. 2.4. Maps and the formulas they preserve. 2.5. Classifying maps by formulas. 2.6. Translations. 2.7. Quantifier elimination. 2.8. Further examples --
3. Structures that look alike. 3.1. Theorems of Skolem. 3.2. Back-and-forth equivalence. 3.3. Games for elementary equivalence. 3.4. Closed games. 3.5. Games and infinitary languages. 3.6. Clubs --
4. Automorphisms. 4.1. Automorphisms. 4.2. Subgroups of small index. 4.3. Imaginary elements. 4.4. Eliminating imaginaries. 4.5. Minimal sets. 4.6. Geometries. 4.7. Almost strongly minimal theories. 4.8. Zilber's configuration --
5. Interpretations. 5.1. Relativisation. 5.2. Pseudo-elementary classes. 5.3. Interpreting one structure in another. 5.4. Shapes and sizes of interpretations. 5.5. Theories that interpret anything. 5.6. Totally transcendental structures. 5.7. Interpreting groups and fields --
6. The first-order case: compactness. 6.1. Compactness for first-order logic. 6.2. Boolean algebras and Stone spaces. 6.3. Types. 6.4. Elementary amalgamation. 6.5. Amalgamation and preservation. 6.6. Expanding the language. 6.7. Stability --
7. The countable case. 7.1. Fraisse's construction. 7.2. Omitting types. 7.3. Countable categoricity. 7.4. [omega]-categorical structures by Fraisse's method --
8. The existential case. 8.1. Existentially closed structures. 8.2. Two methods of construction. 8.3. Model-completeness. 8.4. Quantifier elimination revisited. 8.5. More on e.c. models. 8.6. Amalgamation revisited --
9. The Horn case: products. 9.1. Direct products. 9.2. Presentations. 9.3. Word-constructions. 9.4. Reduced products. 9.5. Ultraproducts. 9.6. The Feferman-Vaught theorem. 9.7. Boolean powers --
10. Saturation. 10.1. The great and the good. 10.2. Big models exist. 10.3. Syntactic characterisations. 10.4. Special models. 10.5. Definability. 10.6. Resplendence. 10.7. Atomic compactness --
11. Combinatorics. 11.1. Indiscernibles. 11.2. Ehrenfeucht-Mostowski models. 11.3. EM models of unstable theories. 11.4. Nonstandard methods. 11.5. Defining well-orderings. 11.6. Infinitary indiscernibles --
12. Expansions and categoricity. 12.1. One-cardinal and two-cardinal theorems. 12.2. Categoricity. 12.3. Cohomology of expansions. 12.4. Counting expansions. 12.5. Relative categoricity. A.1. Modules. A.2. Abelian groups. A.3. Nilpotent groups of class 2. A.4. Groups. A.5. Fields. A.6. Linear orderings.
Series Title: Encyclopedia of mathematics and its applications, v. 42.
Responsibility: Wilfrid Hodges.
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Abstract:

An up-to-date and integrated introduction to model theory, designed to be used for graduate courses (for students who are familiar with first-order logic), and as a reference for more experienced  Read more...

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"...sets forth the basic tools that the fledgling model theorist should master....a new standard reference in this subject." J.M. Plotkin, Mathematical Reviews "...an important contribution to the Read more...

 
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