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A multiverse perspective on the axiom of constructibility

Abstract:
I shall argue that the commonly held V ≠= L via maximize position, which rejects the axiom of constructibility V = L on the basis that it is restrictive, implicitly takes a stand in the pluralist debate in the philosophy of set theory by presuming an absolute background concept of ordinal. The argument appears to lose its force, in contrast, on an upwardly extensible concept of set, in light of the various facts showing that models of set theory generally have extensions to models of V = L inside larger set-Theoretic universes.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1142/9789814571043_0002

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Institution:
University of Oxford
Division:
Humanities Division
Department:
Philosophy
Oxford college:
University College
Role:
Author
Publisher:
World Scientific Publishing Publisher's website
Volume:
25
Pages:
25-45
Series:
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore
Host title:
Infinity and Truth
Publication date:
2014-01-01
DOI:
ISSN:
1793-0758
Source identifiers:
916843
ISBN:
9789814571036
Keywords:
Pubs id:
pubs:916843
UUID:
uuid:8b88341f-8595-4435-ae83-50f540bfb65e
Local pid:
pubs:916843
Deposit date:
2019-12-18

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