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Mathematical Logic

  • Textbook
  • © 1976

Overview

Authors:
  1. J. Donald Monk

    1. Department of Mathematics, University of Colorado, Boulder, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 37)

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About this book

From the Introduction: "We shall base our discussion on a set-theoretical foundation like that used in developing analysis, or algebra, or topology. We may consider our task as that of giving a mathematical analysis of the basic concepts of logic and mathematics themselves. Thus we treat mathematical and logical practice as given empirical data and attempt to develop a purely mathematical theory of logic abstracted from these data."

There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book.

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Table of contents (32 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    1. Introduction

      • J. Donald Monk
      Pages 1-9

  3. Recursive Function Theory

    1. Front Matter

      Pages 11-13
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    2. Turing Machines

      • J. Donald Monk
      Pages 14-25

    3. Elementary recursive and primitive recursive functions

      • J. Donald Monk
      Pages 26-44

    4. Recursive Functions; Turing Computability

      • J. Donald Monk
      Pages 45-68

    5. Markov Algorithms

      • J. Donald Monk
      Pages 69-75

    6. Recursion Theory

      • J. Donald Monk
      Pages 76-91

    7. Recursively Enumerable Sets

      • J. Donald Monk
      Pages 92-104

    8. Survey of Recursion Theory

      • J. Donald Monk
      Pages 105-111

  4. Elements of Logic

    1. Front Matter

      Pages 113-114
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    2. Sentential Logic

      • J. Donald Monk
      Pages 115-140

    3. Boolean Algebra

      • J. Donald Monk
      Pages 141-161

    4. Syntactics of First-order Languages

      • J. Donald Monk
      Pages 162-193

    5. Some Basic Results of First-order Logic

      • J. Donald Monk
      Pages 194-218

    6. Cylindric Algebras

      • J. Donald Monk
      Pages 219-229

  5. Decidable and Undecidable Theories

    1. Front Matter

      Pages 231-232
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    2. Some Decidable Theories

      • J. Donald Monk
      Pages 233-243

    3. Implicit Definability in Number Theories

      • J. Donald Monk
      Pages 244-261

    4. General Theory of Undecidability

      • J. Donald Monk
      Pages 262-278
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Authors and Affiliations

  • Department of Mathematics, University of Colorado, Boulder, USA

    J. Donald Monk

Bibliographic Information

  • Book Title: Mathematical Logic

  • Authors: J. Donald Monk

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-9452-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1976

  • Hardcover ISBN: 978-0-387-90170-1Published: 07 September 1976

  • Softcover ISBN: 978-1-4684-9454-9Published: 15 July 2012

  • eBook ISBN: 978-1-4684-9452-5Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: X, 532

  • Topics: Mathematical Logic and Foundations

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