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Computable Structure Theory
Within the Arithmetic

$125.00 (C)

Part of Perspectives in Logic

  • Date Published: June 2021
  • availability: Available
  • format: Hardback
  • isbn: 9781108423298

$ 125.00 (C)

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About the Authors
  • In mathematics, we know there are some concepts - objects, constructions, structures, proofs - that are more complex and difficult to describe than others. Computable structure theory quantifies and studies the complexity of mathematical structures, structures such as graphs, groups, and orderings. Written by a contemporary expert in the subject, this is the first full monograph on computable structure theory in 20 years. Aimed at graduate students and researchers in mathematical logic, it brings new results of the author together with many older results that were previously scattered across the literature and presents them all in a coherent framework, making it easier for the reader to learn the main results and techniques in the area for application in their own research. This volume focuses on countable structures whose complexity can be measured within arithmetic; a forthcoming second volume will study structures beyond arithmetic.

    • Makes the subject accessible to graduate students and researchers in logic, from the basic concepts to the frontiers of current research
    • Presents the main results and techniques in computable structure theory together in a coherent framework for the first time in 20 years
    • Includes new work of the author as well as new perspectives on older results.
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    Reviews & endorsements

    ‘This exceptionally well-written book is the first modern monograph on computable structure theory in 20 years … The author succeeds in bringing together new and old results and presenting them in a coherent framework, making it easy for the reader to learn the main results and techniques in the area for application in their own research.’ Alexandra Andreeva Soskova, MathSciNet

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    Product details

    • Date Published: June 2021
    • format: Hardback
    • isbn: 9781108423298
    • length: 250 pages
    • dimensions: 240 x 162 x 18 mm
    • weight: 0.49kg
    • availability: Available
  • Table of Contents

    1. Structures
    2. Relations
    3. Existentially-Atomic Models
    4. Generic Presentations
    5. Degree Spectra
    6. Comparing Structures and Classes of Structures
    7. Finite-Injury Constructions
    8. Computable Categoricity
    9. The Jump of a Structure
    10. ∑-Small Classes

  • Author

    Antonio Montalbán, University of California, Berkeley
    Antonio Montalbán is Professor of Mathematics at the University of California, Berkeley.

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