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THE SET-THEORETIC MULTIVERSE

Published online by Cambridge University Press:  09 August 2012

JOEL DAVID HAMKINS*
Affiliation:
Department of Philosophy, New York University, Mathematics Program, The Graduate Center of The City University of New York, and Department of Mathematics, The College of Staten Island of CUNY
*
*DEPARTMENT OF PHILOSOPHY, NEW YORK UNIVERSITY, 5 WASHINGTON PLACE, NEW YORK, NY 10003, MATHEMATICS PROGRAM, THE GRADUATE CENTER OF THE CITY UNIVERSITY OF NEW YORK, 365 FIFTH AVENUE, NEW YORK, NY 10016, DEPARTMENT OF MATHEMATICS, THE COLLEGE OF STATEN ISLAND OF CUNY, STATEN ISLAND, NY 10314, E-mail: jhamkins@gc.cuny.edu, http://jdh.hamkins.org
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Abstract

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The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous range of set-theoretic possibilities, a phenomenon that challenges the universe view. In particular, I argue that the continuum hypothesis is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2012

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