Stationary reflection and level by level equivalence
نویسندگان
چکیده
منابع مشابه
Stationary Reflection and Level by Level Equivalence
We force and construct a model in which level by level equivalence between strong compactness and supercompactness holds, along with certain additional “inner model like” properties. In particular, in this model, the class of Mahlo cardinals reflecting stationary sets is the same as the class of weakly compact cardinals, and every regular Jonsson cardinal is weakly compact. On the other hand, w...
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Starting from a model V “ZFC + GCH + κ is supercompact + No cardinal is supercompact up to a measurable cardinal”, we force and construct a model V P such that V P “ZFC + κ is supercompact + No cardinal is supercompact up to a measurable cardinal + δ is measurable iff δ is tall” in which level by level equivalence between strong compactness and supercompactness holds. This extends and generaliz...
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We force and construct a model in which GCH and level by level equivalence between strong compactness and supercompactness hold, along with certain additional “L-like” combinatorial principles. In particular, this model satisfies the following properties: 1. ♦δ holds for every successor and Mahlo cardinal δ. 2. There is a stationary subset S of the least supercompact cardinal κ0 such that for e...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2009
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm115-1-10