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An Invitation to Model Theory

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  • Publication planned for: June 2019
  • availability: Not yet published - available from June 2019
  • format: Paperback
  • isbn: 9781316615553
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  • Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.

    • Suitable for use as an undergraduate- or Masters-level course in model theory, unlike traditional graduate-level texts
    • Contains many exercises of varying difficulty, from bookwork to more substantial projects
    • Presents model theory in the context of undergraduate mathematics via definable sets in familiar structures
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    28th Jan 2019 by Niconi

    I am looking forward to it and hope to take more in.

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    Product details

    • Publication planned for: June 2019
    • format: Paperback
    • isbn: 9781316615553
    • length: 194 pages
    • dimensions: 227 x 151 x 12 mm
    • weight: 0.3kg
    • contains: 5 b/w illus.
    • availability: Not yet published - available from June 2019
  • Table of Contents

    Preface
    Part I. Languages and Structures:
    1. Structures
    2. Terms
    3. Formulas
    4. Definable sets
    5. Substructures and quantifiers
    Part II. Theories and Compactness:
    6. Theories and axioms
    7. The complex and real fields
    8. Compactness and new constants
    9. Axiomatisable classes
    10. Cardinality considerations
    11. Constructing models from syntax
    Part III. Changing Models:
    12. Elementary substructures
    13. Elementary extensions
    14. Vector spaces and categoricity
    15. Linear orders
    16. The successor structure
    Part IV. Characterising Definable Sets:
    17. Quantifier elimination for DLO
    18. Substructure completeness
    19. Power sets and Boolean algebras
    20. The algebras of definable sets
    21. Real vector spaces and parameters
    22. Semi-algebraic sets
    Part V. Types:
    23. Realising types
    24. Omitting types
    25. Countable categoricity
    26. Large and small countable models
    27. Saturated models
    Part VI. Algebraically Closed Fields:
    28. Fields and their extensions
    29. Algebraic closures of fields
    30. Categoricity and completeness
    31. Definable sets and varieties
    32. Hilbert's Nullstellensatz
    Bibliography
    Index.

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    An Invitation to Model Theory

    Jonathan Kirby

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  • Author

    Jonathan Kirby, University of East Anglia
    Jonathan Kirby is a Senior Lecturer in Mathematics at the University of East Anglia. His main research is in model theory and its interactions with algebra, number theory, and analysis, with particular interest in exponential functions. He has taught model theory at the University of Oxford, the University of Illinois, Chicago, and the University of East Anglia.

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