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© 1999

Recursive Functions and Metamathematics

Problems of Completeness and Decidability, Gödel’s Theorems

Book

Part of the Synthese Library book series (SYLI, volume 286)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Roman Murawski
    Pages 1-17
  3. Roman Murawski
    Pages 19-95
  4. Roman Murawski
    Pages 97-210
  5. Roman Murawski
    Pages 211-280
  6. Roman Murawski
    Pages 281-340
  7. Back Matter
    Pages 341-395

About this book

Introduction

Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography.
Readership: Scholars and advanced students of logic, mathematics, philosophy of science.

Keywords

logic mathematical logic mathematics philosophy of science science

Authors and affiliations

  1. 1.Adam Mickiewicz UniversityPoznańPoland

Bibliographic information

  • Book Title Recursive Functions and Metamathematics
  • Book Subtitle Problems of Completeness and Decidability, Gödel’s Theorems
  • Authors Roman Murawski
  • Series Title Synthese Library
  • DOI https://doi.org/10.1007/978-94-017-2866-9
  • Copyright Information Springer Science+Business Media B.V. 1999
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-7923-5904-3
  • Softcover ISBN 978-90-481-5298-8
  • eBook ISBN 978-94-017-2866-9
  • Edition Number 1
  • Number of Pages XII, 395
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Logic
    Mathematical Logic and Foundations
    Philosophy of Science
    Theory of Computation
  • Buy this book on publisher's site