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Logical Foundations of Mathematics and Computational Complexity

A Gentle Introduction

  • Pavel Pudlák

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Pavel Pudlák
    Pages 1-64
  3. Pavel Pudlák
    Pages 65-155
  4. Pavel Pudlák
    Pages 157-253
  5. Pavel Pudlák
    Pages 255-364
  6. Pavel Pudlák
    Pages 365-493
  7. Pavel Pudlák
    Pages 495-581
  8. Pavel Pudlák
    Pages 583-665
  9. Back Matter
    Pages 667-695

About this book

Introduction

The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability.

Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs.

Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.

Keywords

Complexity of Proofs Computational Complexity Foundations of Mathematics Incompleteness Theorems Mathematical Logic Set-Theoretical Foundations

Authors and affiliations

  • Pavel Pudlák
    • 1
  1. 1.ASCRPraha 1Czech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-00119-7
  • Copyright Information Springer International Publishing Switzerland 2013
  • Publisher Name Springer, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-00118-0
  • Online ISBN 978-3-319-00119-7
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site
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