The Axiom of Determinancy Implies Dependent Choices in L(R)
نویسنده
چکیده
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') it follows that DC (as well as AC') is independent relative to ZF + AD. It is finally shown (jointly with H. Woodin) that ZF + AD + DCR, where DCR 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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عنوان ژورنال:
- J. Symb. Log.
دوره 49 شماره
صفحات -
تاریخ انتشار 1984