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.
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| 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. | |||||||||
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| 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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