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The hyperuniverse project and maximality

edited byCarolin Antos Radek Honzik Claudio Ternullo Sy David Friedman

Abstract

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.

Details | Table of Contents

Class forcing in class theory Carolin Antos

pp.1-16

https://doi.org/10.1007/978-3-319-62935-3_1

Hyperclass forcing in Morse-Kelley class theory Carolin Antos Sy David Friedman

pp.17-46

https://doi.org/10.1007/978-3-319-62935-3_2

Multiverse conceptions in set theory Carolin Antos Radek Honzik Claudio Ternullo Sy David Friedman

pp.47-73

https://doi.org/10.1007/978-3-319-62935-3_3

Evidence for set-theoretic truth and the hyperuniverse programme Sy David Friedman

pp.75-107

https://doi.org/10.1007/978-3-319-62935-3_4

On the set-generic multiverse Sy David Friedman Sakaé Fuchino Hiroshi Sakai

pp.109-124

https://doi.org/10.1007/978-3-319-62935-3_5

On strong forms of reflection in set theory Radek Honzik

pp.125-134

https://doi.org/10.1007/978-3-319-62935-3_6

Definability of satisfaction in outer models Radek Honzik Sy David Friedman

pp.135-160

https://doi.org/10.1007/978-3-319-62935-3_7

The search for new axioms in the hyperuniverse programme Claudio Ternullo Sy David Friedman

pp.161-183

https://doi.org/10.1007/978-3-319-62935-3_8

Explaining maximality through the hyperuniverse programme Claudio Ternullo Sy David Friedman

pp.185-204

https://doi.org/10.1007/978-3-319-62935-3_9

Large cardinals and the continuum hypothesis Radek Honzik

pp.205-226

https://doi.org/10.1007/978-3-319-62935-3_10

Gödel's Cantorianism Claudio Ternullo

pp.227-258

https://doi.org/10.1007/978-3-319-62935-3_11

Remarks on Buzaglo's concept expansion and Cantor's transfinite Claudio Ternullo

pp.259-270

https://doi.org/10.1007/978-3-319-62935-3_12

Publication details

Publisher: Springer

Place: Dordrecht

Year: 2018

Pages: 270

ISBN (hardback): 978-3-319-62934-6

ISBN (digital): 978-3-319-62935-3

Full citation:

Antos Carolin, Honzik Radek, Ternullo Claudio, Friedman Sy David (2018) The hyperuniverse project and maximality. Dordrecht, Springer.