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What is the theory ZFC without power set?

Abstract:

We show that the theory ZFC, consisting of the usual axioms of ZFC but with the power set axiom removed—specifically axiomatized by extensionality, foundation, pairing, union, infinity, separation, replacement and the assertion that every set can be well-ordered—is weaker than commonly supposed and is inadequate to establish several basic facts often desired in its context. For example, there are models of ZFC in which ω 1 is singular, in which every set of reals is countable, yet ω 1 exists,...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1002/malq.201500019

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Institution:
University of Oxford
Division:
Humanities Division
Department:
Philosophy
Oxford college:
University College
Role:
Author
Publisher:
Wiley Publisher's website
Journal:
Mathematical Logic Quarterly Journal website
Volume:
62
Issue:
4-5
Pages:
391-406
Publication date:
2016-07-25
Acceptance date:
2015-08-22
DOI:
EISSN:
1521-3870
ISSN:
0942-5616
Source identifiers:
916656
Language:
English
Keywords:
Pubs id:
pubs:916656
UUID:
uuid:fc1a16c9-b18a-44f3-a568-55e8c78608ed
Local pid:
pubs:916656
Deposit date:
2019-12-18

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