Multiverse conceptions in set theory

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F15%3A10319880" target="_blank" >RIV/00216208:11210/15:10319880 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11229-015-0819-9" target="_blank" >http://dx.doi.org/10.1007/s11229-015-0819-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11229-015-0819-9" target="_blank" >10.1007/s11229-015-0819-9</a>

Result language
angličtina
Original language name
Multiverse conceptions in set theory
Original language description
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 toclassify 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 SymbLogic 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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