Model theory /

Model theory /

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Bibliographic Details
Author / Creator:Chang, Chen Chung, 1927-
Edition:Dover ed.
Imprint:Mineola, N.Y. : Dover Publications, 2012.
Description:xvi, 650 p. : ill. ; 24 cm
Language:English
Subject:
Model theory.
Model theory.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/9333051
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Other authors / contributors:Keisler, H. Jerome.
ISBN:9780486488219
0486488217
Notes:Originally published: 3rd ed. Amsterdam ; New York : North-Holland Press, 1990, in series: Studies in logic and the foundations of mathematics ; v. 73.
Includes bibliographical references (p. 623-640) and index.
Table of Contents:
  • Chapter 1. Introduction
  • 1.1. What is model theory?
  • 1.2. Model theory for sentential logic
  • 1.3. Languages, models and satisfaction
  • 1.4. Theories and examples of theories
  • 1.5. Elimination of quantifiers
  • Chapter 2. Models constructed from constants
  • 2.1. Completeness and compactness
  • 2.2. Refinements of the method. Omitting types and interpolation theorems
  • 2.3. Countable models of complete theories
  • 2.4. Recursively saturated models
  • 2.5. Lindstrom's characterization of first order logic
  • Chapter 3. Further model-theoretic constructions
  • 3.1. Elementary extensions and elementary chains
  • 3.2. Applications of elementary chains
  • 3.3. Skolem functions and indiscernibles
  • 3.4. Some examples
  • 3.5. Model completeness
  • Chapter 4. Ultraproducts
  • 4.1. The fundamental theorem
  • 4.2. Measurable cardinals
  • 4.3. Regular ultrapowers
  • 4.4. Nonstandard universes
  • Chapter 5. Saturated and special models
  • 5.1. Saturated and special models
  • 5.2. Preservation theorems
  • 5.3. Applications of special models to the theory of definability
  • 5.4. Applications to field theory
  • 5.5. Application to Boolean algebras
  • Chapter 6. More about ultraproducts and generalizations
  • 6.1. Ultraproducts which are saturated
  • 6.2. Direct products, reduced products, and Horn sentences
  • 6.3. Direct products, reduced products, and Horn sentences (continued)
  • 6.4. Limit ultrapowers and complete extensions
  • 6.5. Iterated ultrapowers
  • Chapter 7. Selected topics
  • 7.1. Categoricity in power
  • 7.2. An extension of Ramsey's theorem and applications; some two-cardinal theorems
  • 7.3. Models of large cardinality
  • 7.4. Large cardinals and the constructible universe
  • Appendix A. Set theory
  • Appendix B. Open problems in classical model theory
  • Historical notes
  • References
  • Additional references
  • Index of definitions
  • Index of symbols

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