Compact spaces, compact cardinals, and elementary submodels
نویسندگان
چکیده
منابع مشابه
Compact spaces, elementary submodels, and the countable chain condition
Given a space 〈X,J 〉 in an elementary submodel M of H(θ), define XM to be X ∩ M with the topology generated by {U ∩ M : U ∈ J ∩ M}. It is established, using anti-large-cardinals assumptions, that if XM is compact and its regular open algebra is isomorphic to that of a continuous image of some power of the two-point discrete space, then X = XM . Assuming CH+SCH (the Singular Cardinals Hypothesis...
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We show relative to strong hypotheses that patterns of compact cardinals in the universe, where a compact cardinal is one which is either strongly compact or supercompact, can be virtually arbitrary. Specifically, we prove if V |= “ZFC + Ω is the least inaccessible limit of measurable limits of supercompact cardinals + f : Ω → 2 is a function”, then there is a partial ordering P ∈ V so that for...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2003
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(02)00214-6