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International Studies in Phenomenology and Philosophy

Book | Chapter

179391

Multiverse conceptions in set theory

Carolin AntosRadek Honzik Claudio Ternullo Sy David Friedman

pp. 47-73

Abstract

We review different conceptions of the set-theoretic multiverse and evaluate their features and strengths. In Sect. 1, we set the stage by briefly discussing the opposition between the "universe view' and the "multiverse view'. Furthermore, we propose to classify multiverse conceptions in terms of their adherence to some form of mathematical realism. In Sect. 2, we use this classification to review four major conceptions. Finally, in Sect. 3, we focus on the distinction between actualism and potentialism with regard to the universe of sets, then we discuss the Zermelian view, featuring a "vertical' multiverse, and give special attention to this multiverse conception in light of the hyperuniverse programme introduced in Arrigoni-Friedman (Bull Symb Logic 19(1):77–96, 2013). We argue that the distinctive feature of the multiverse conception chosen for the hyperuniverse programme is its utility for finding new candidates for axioms of set theory.

Publication details

Published in:

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

Pages: 47-73

DOI: 10.1007/978-3-319-62935-3_3

Full citation:

Antos Carolin, Honzik Radek, Ternullo Claudio, Friedman Sy David (2018) „Multiverse conceptions in set theory“, In: C. Antos, R. Honzik, C. Ternullo & S. Friedman (eds.), The hyperuniverse project and maximality, Dordrecht, Springer, 47–73.