The axiom of determinacy implies dependent choices in L(R)
The axiom of determinacy implies dependent choices in L(R)
复制标题
确定性公理意味着 L(R) 中的依赖选择
DOI：
10.2307/2274099
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发表时间：
1984
影响因子：
0.6
通讯作者：
A. Kechris
中科院分区：
文献类型：
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作者：
A. Kechris
摘要 我们证明了如下主定理：ZF + AD + V ⇒ L(R) ⇒ DC。作为一个推论，我们有Con(ZF + AD) ⇒ Con(ZF + AD + DC)。结合伍丁的结果Con(ZF + AD) ⇒ Con(ZF + AD + ¬ ACω)，可以得出DC（以及ACω）相对于ZF + AD是独立的。最后（与H. 伍丁共同）表明ZF + AD + ¬DCR（其中DCR是限制在实数上的DC）蕴含ZF + AD + DC的一致性，实际上蕴含R#（即L(R)的锐）存在。
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 + ¬ ACω) it follows that DC (as well as ACω) 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.