A Model of the Axiom of Determinacy in Which Every Set of Reals Is Universally Baire (draft)
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چکیده
The consistency of the theory ZF+AD+“every set of reals is universally Baire” is proved relative to ZFC + “there is a cardinal λ that is a limit of Woodin cardinals and of strong cardinals.” The proof is based on the derived model construction, which was used by Woodin to show that the theory ZF+AD+“every set of reals is Suslin” is consistent relative to ZFC+“there is a cardinal λ that is a limit of Woodin cardinals and of <λ-strong cardinals.” The Σ1 reflection property of our model is proved using genericity iterations as in Neeman [7] and Steel [8].
منابع مشابه
Descriptive Inner Model Theory , Large Cardinals , and Combinatorics Research Statement Nam Trang
My research interest is in mathematical logic and set theory. My current research focuses on studying the connections between inner models, (determined) sets of reals, hybrid structures (such as HOD1 of determinacy models), forcing, and strong combinatorial principles (such as the Proper Forcing Axiom (PFA), (generalizations of) the tree property, the Unique Branch Hypothesis (UBH)). I’m also i...
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تاریخ انتشار 2014