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Recursion-Theoretic Hierarchies

$155.00 (C)

Part of Perspectives in Logic

  • Date Published: March 2017
  • availability: Available
  • format: Hardback
  • isbn: 9781107168244

$ 155.00 (C)
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About the Authors
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. The theory set out in this volume, the ninth publication in the Perspectives in Logic series, is the result of the meeting and common development of two currents of mathematical research: descriptive set theory and recursion theory. Both are concerned with notions of definability and with the classification of mathematical objects according to their complexity. These are the common themes which run through the topics discussed here. The author develops a general theory from which the results of both areas can be derived, making these common threads clear.

    • Contains a series of challenging exercises to supplement the material in the book
    • Can be used for a variety of courses in areas such as recursion theory, descriptive set theory, or theory of definability
    • Suitable for those who have completed a first course in mathematical logic
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    Product details

    • Date Published: March 2017
    • format: Hardback
    • isbn: 9781107168244
    • dimensions: 240 x 163 x 37 mm
    • weight: 0.93kg
    • contains: 7 b/w illus.
    • availability: Available
  • Table of Contents

    Introduction
    Part I. Basic Notations of Definability:
    1. Groundwork
    2. Ordinary recursion theory
    3. Hierarchies and definability
    Part II. The Analytical and Projective Hierarchies:
    4. The first level
    5. Δ^1_2 and beyond
    Part III. Generalized Recursion Theories:
    6. Recursion in a type-2 functional
    7. Recursion in a type-3 functional
    8. Recursion on ordinals
    Epilogue
    References
    Global notational conventions
    Special notations
    Index.

  • Author

    Peter G. Hinman, University of Michigan, Ann Arbor
    Peter G. Hinman works in the Department of Mathematics at the University of Michigan, Ann Arbor.

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