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The Axiom of Determinacy Implies Dependent Choices in L(R)

Kechris, Alexander S. (1984) The Axiom of Determinacy Implies Dependent Choices in L(R). Journal of Symbolic Logic, 49 (1). pp. 161-173. ISSN 0022-4812. https://resolver.caltech.edu/CaltechAUTHORS:20130528-083650112

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Abstract

We prove the following Main Theorem: ZF+AD+V=L(R)⇒DC. As a corollary we have that Con(ZF+AD)⇒Con(ZF+AD+DC). Combined with the result of Woodin that Con(ZF+AD)⇒Con(ZF+AD+¬AC^ω) it follows that DC (as well as AC^ω) is independent relative to ZF+AD. It is finally shown (jointly with H. Woodin) that ZF+AD+¬DC_R, where DC_R is DC restricted to reals, implies the consistency of ZF+AD+DC, in fact implies R^# (i.e. the sharp of L(R)) exists.


Item Type:Article
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http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jsl/1183741483PublisherUNSPECIFIED
http://www.jstor.org/stable/2274099PublisherUNSPECIFIED
Alternate Title:The Axiom of Determinancy Implies Dependent Choices in L(R)
Additional Information:© 1984, Association for Symbolic Logic. Received April 29, 1982. Research partially supported by NSF Grant No. MCS-8117804. The author is an A. P. Sloan Foundation Fellow.
Funders:
Funding AgencyGrant Number
NSFMCS-8117804
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MathSciNet ReviewMR0736611
Issue or Number:1
Record Number:CaltechAUTHORS:20130528-083650112
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130528-083650112
Official Citation:The Axiom of Determinancy Implies Dependent Choices in L(R) Alexander S. Kechris; 161-173
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38675
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:28 May 2013 15:50
Last Modified:03 Oct 2019 04:59

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