Publikation: Multiverse conceptions in set theory
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2015
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Synthese. 2015, 192(8), pp. 2463-2488. ISSN 0039-7857. eISSN 1573-0964. Available under: doi: 10.1007/s11229-015-0819-9
Zusammenfassung
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 and 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.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
100 Philosophie
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Set theory, Universe of sets, Set-theoretic multiverse, Hyperuniverse programme, New axioms of set theory
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ANTOS, Carolin, Sy-David FRIEDMAN, Radek HONZIK, Claudio TERNULLO, 2015. Multiverse conceptions in set theory. In: Synthese. 2015, 192(8), pp. 2463-2488. ISSN 0039-7857. eISSN 1573-0964. Available under: doi: 10.1007/s11229-015-0819-9BibTex
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title={Multiverse conceptions in set theory},
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