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The Hyperuniverse Project and Maximality

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  • © 2018

Overview

Editors:
  1. Carolin Antos

    1. Zukunftskolleg, University of Konstanz, Konstanz, Germany

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  2. Sy-David Friedman

    1. Kurt Gödel Research Center, University of Vienna, Vienna, Austria

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  3. Radek Honzik

    1. Department of Logic, Charles University, Prague, Czech Republic

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  4. Claudio Ternullo

    1. Kurt Gödel Research Center, University Wien, Wien, Austria

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  • First overview of the Hyperuniverse Programme

  • Illustrates its mathematical content and implications

  • Provides a robust and convincing philosophical justification for the Hyperuniverse Programme

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xi
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  2. Class Forcing in Class Theory

    • Carolin Antos
    Pages 1-16

  3. Hyperclass Forcing in Morse-Kelley Class Theory

    • Carolin Antos, Sy-David Friedman
    Pages 17-46

  4. Multiverse Conceptions in Set Theory

    • Carolin Antos, Sy-David Friedman, Radek Honzik, Claudio Ternullo
    Pages 47-73

  5. Evidence for Set-Theoretic Truth and the Hyperuniverse Programme

    • Sy-David Friedman
    Pages 75-107

  6. On the Set-Generic Multiverse

    • Sy-David Friedman, Sakaé Fuchino, Hiroshi Sakai
    Pages 109-124

  7. On Strong Forms of Reflection in Set Theory

    • Sy-David Friedman, Radek Honzik
    Pages 125-134

  8. Definability of Satisfaction in Outer Models

    • Sy-David Friedman, Radek Honzik
    Pages 135-160

  9. The Search for New Axioms in the Hyperuniverse Programme

    • Sy-David Friedman, Claudio Ternullo
    Pages 161-183

  10. Explaining Maximality Through the Hyperuniverse Programme

    • Sy-David Friedman, Claudio Ternullo
    Pages 185-204

  11. Large Cardinals and the Continuum Hypothesis

    • Radek Honzik
    Pages 205-226

  12. Gödel’s Cantorianism

    • Claudio Ternullo
    Pages 227-258

  13. Remarks on Buzaglo’s Concept Expansion and Cantor’s Transfinite

    • Claudio Ternullo
    Pages 259-270
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Keywords

About this book

This collection documents the work of the Hyperuniverse Project which is a new approach to set-theoretic truth based on justifiable principles and which leads to the resolution of many questions independent from ZFC.

The contributions give an overview of the program, illustrate its mathematical content and implications, and also discuss its philosophical assumptions. It will thus be of wide appeal among mathematicians and philosophers with an interest in the foundations of set theory.

The Hyperuniverse Project was supported by the John Templeton Foundation from January 2013 until September 2015

Editors and Affiliations

  • Zukunftskolleg, University of Konstanz, Konstanz, Germany

    Carolin Antos

  • Kurt Gödel Research Center, University of Vienna, Vienna, Austria

    Sy-David Friedman

  • Department of Logic, Charles University, Prague, Czech Republic

    Radek Honzik

  • Kurt Gödel Research Center, University Wien, Wien, Austria

    Claudio Ternullo

About the editors

Professor Sy David Friedman is head of the "Kurt Gödel Research Center for Mathematical Logic", Vienna.

Bibliographic Information

  • Book Title: The Hyperuniverse Project and Maximality

  • Editors: Carolin Antos, Sy-David Friedman, Radek Honzik, Claudio Ternullo

  • DOI: https://doi.org/10.1007/978-3-319-62935-3

  • Publisher: Birkhäuser Cham

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

  • Copyright Information: Springer International Publishing AG 2018

  • Hardcover ISBN: 978-3-319-62934-6Published: 07 February 2018

  • Softcover ISBN: 978-3-319-87432-6Published: 04 June 2019

  • eBook ISBN: 978-3-319-62935-3Published: 30 January 2018

  • Edition Number: 1

  • Number of Pages: XI, 265

  • Number of Illustrations: 11 b/w illustrations

  • Topics: Mathematical Logic and Foundations, Philosophy of Mathematics

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