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Recursive Functions and Metamathematics

Problems of Completeness and Decidability, Gödel’s Theorems

  • Book
  • © 1999

Overview

Authors:
  1. Roman Murawski

    1. Adam Mickiewicz University, Poznań, Poland

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Roman Murawski
    Pages 1-17

  3. Recursive Functions

    • Roman Murawski
    Pages 19-95

  4. Gödel’s Incompleteness Theorems

    • Roman Murawski
    Pages 97-210

  5. Decidability Theory

    • Roman Murawski
    Pages 211-280

  6. Philosophical Comments

    • Roman Murawski
    Pages 281-340

  7. Back Matter

    Pages 341-395
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Keywords

About this book

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.

Authors and Affiliations

  • Adam Mickiewicz University, Poznań, Poland

    Roman Murawski

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

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1999

  • Hardcover ISBN: 978-0-7923-5904-3Published: 30 September 1999

  • Softcover ISBN: 978-90-481-5298-8Published: 06 December 2010

  • eBook ISBN: 978-94-017-2866-9Published: 14 March 2013

  • Series ISSN: 0166-6991

  • Series E-ISSN: 2542-8292

  • Edition Number: 1

  • Number of Pages: XII, 395

  • Topics: Logic, Mathematical Logic and Foundations, Philosophy of Science, Theory of Computation

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