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Diagonalization in Formal Mathematics

  • Book
  • © 2020

Overview

Authors:
  1. Paulo Guilherme Santos

    1. Universidade Nova de Lisboa, Lisboa, Portugal

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  • Publication in the field of natural sciences

Part of the book series: BestMasters (BEST)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-X
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  2. Preliminaries

    • Paulo Guilherme Santos
    Pages 11-18

  3. Introduction

    • Paulo Guilherme Santos
    Pages 19-24

  4. Two uses of the Diagonalization Lemma

    • Paulo Guilherme Santos
    Pages 25-39

  5. Yablo’s Paradox and Self-Reference

    • Paulo Guilherme Santos
    Pages 41-51

  6. Smullyan’s Theorem, Löb’s Theorem, and a General Approach to Paradoxes

    • Paulo Guilherme Santos
    Pages 53-70

  7. General Theory of Diagonalization

    • Paulo Guilherme Santos
    Pages 71-75

  8. Mathematical Examples

    • Paulo Guilherme Santos
    Pages 77-90

  9. Conclusions and Future Work

    • Paulo Guilherme Santos
    Pages 91-93

  10. Back Matter

    Pages 95-99
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Keywords

About this book

In this book, Paulo Guilherme Santos studies diagonalization in formal mathematics from logical aspects to everyday mathematics. He starts with a study of the diagonalization lemma and its relation to the strong diagonalization lemma. After that, Yablo’s paradox is examined, and a self-referential interpretation is given. From that, a general structure of diagonalization with paradoxes is presented. Finally, the author studies a general theory of diagonalization with the help of examples from mathematics.

Authors and Affiliations

  • Universidade Nova de Lisboa, Lisboa, Portugal

    Paulo Guilherme Santos

About the author

Paulo Guilherme Santos is currently a PhD student at FCT, Universidade Nova de Lisboa, Portugal and at University of Tübingen, Germany. His field of work is logic, e.g. formal arithmetic, provability logic, provability predicates, and paradoxes.

Bibliographic Information

  • Book Title: Diagonalization in Formal Mathematics

  • Authors: Paulo Guilherme Santos

  • Series Title: BestMasters

  • DOI: https://doi.org/10.1007/978-3-658-29111-2

  • Publisher: Springer Spektrum Wiesbaden

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2020

  • Softcover ISBN: 978-3-658-29110-5Published: 05 January 2020

  • eBook ISBN: 978-3-658-29111-2Published: 04 January 2020

  • Series ISSN: 2625-3577

  • Series E-ISSN: 2625-3615

  • Edition Number: 1

  • Number of Pages: X, 89

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Mathematical Logic and Foundations, Logic

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