Published March 1984
| Published
Journal Article
Open
The Axiom of Determinacy Implies Dependent Choices in L(R)
- Creators
-
Kechris, Alexander S.
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.
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.Attached Files
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Additional details
- Alternative title
- The Axiom of Determinancy Implies Dependent Choices in L(R)
- Eprint ID
- 38675
- Resolver ID
- CaltechAUTHORS:20130528-083650112
- MCS-8117804
- NSF
- Created
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2013-05-28Created from EPrint's datestamp field
- Updated
-
2019-10-03Created from EPrint's last_modified field
- Other Numbering System Name
- MathSciNet Review
- Other Numbering System Identifier
- MR0736611