UID:
almafu_9959240275502883
Format:
1 online resource (xiii, 772 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88167-1
,
0-511-94151-X
,
1-107-10238-3
,
1-107-09384-8
,
1-107-08759-7
,
0-511-55157-6
Series Statement:
Encyclopedia of mathematics and its applications ; v. 42
Content:
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, geometry, algebra (in particular group theory), and computer science (e.g. logic programming and specification). Professor Hodges emphasises definability and methods of construction, and introduces the reader to advanced topics such as stability. He also provides the reader with much historical information and a full bibliography, enhancing the book's use as a reference.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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Cover; Half-title; Encyclopedia of mathematics and its applications; Title; Copyright; Contents; Introduction; Note on notation; 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; History And Bibliography; 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; History and bibliography
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3 Structures that look alike3.1 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; History and bibliography; 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 Zil'ber's configuration; History and bibliography; 5 Interpretations; 5.1 Relativisation; 5.2 Pseudo-elementary Classes; 5.3 Interpreting one structure in another
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5.4 Shapes and sizes of interpretations5.5 Theories that interpret anything; 5.6 Totally transcendental structures; 5.7 Interpreting groups and fields; History and bibliography; 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; History and bibliography; 7 The countable case; 7.1 Fraisse's construction; 7.2 Omitting types; 7.3 Countable categoricity; 7.4 Cocategorical structures by fraisse's method
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History and bibliography8 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; History and bibliography; 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; History and bibliography; 10 Saturation; 10.1 The great and the good; 10.2 Big models exist; 10.3 Syntactic characterisations; 10.4 Special models
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10.5 Definability10.6 Resplendence; 10.7 Atomic compactness; History and bibliography; 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; History and bibliography; 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; History and bibliography; Appendix: Examples; A.1 Modules; A.2 Abelian groups
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A.3 Nilpotent groups of class 2
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English
Additional Edition:
ISBN 0-521-06636-0
Additional Edition:
ISBN 0-521-30442-3
Language:
English
URL:
https://doi.org/10.1017/CBO9780511551574
