Inflation with Ω≠1
نویسندگان
چکیده
منابع مشابه
Games of Length Ω1
We prove determinacy for open length ω1 games. Going further we introduce, and prove determinacy for, a stronger class of games of length ω1, with payoff conditions involving the entire run, the club filter on ω1, and a sequence of ω1 disjoint stationary subsets of ω1. The determinacy proofs use an iterable model with a class of indiscernible Woodin cardinals, and we show that the games precise...
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This paper is centered on an extremely general problem: Problem. Is it consistent (perhaps modulo large cardinals) that a locally compact space X must be the union of countably many ω-bounded subspaces if every closed discrete subspace of X is countable [in other words, if X is ω1-compact]? A space is ω-bounded if every countable subset has compact closure. This is a strengthening of countable ...
متن کاملDeterminacy from Strong Compactness of Ω1
In the absence of the Axiom of Choice, the “small” cardinal ω1 can exhibit properties more usually associated with large cardinals, such as strong compactness and supercompactness. For a local version of strong compactness, we say that ω1 is Xstrongly compact (where X is any set) if there is a fine, countably complete measure on ℘ω1(X). Working in ZF + DC, we prove that the ℘(ω1)-strong compact...
متن کاملClasses of structures with universe a subset of ω1
We continue recent work on computable structure theory in the setting of ω1. We prove the analog of a result from [5] saying that isomorphism of computable structures lies “on top” among Σ1 equivalence relations relations on ω. Our equivalence relations are on ω1. In the standard setting, Σ1 sets are characterized in terms of paths through trees. In the setting of ω1, we use a new characterizat...
متن کاملOn Perfect Pre–images of Ω1
We show that PFA implies that every perfect pre–image of ω1 of countable tightness contains a closed copy of ω1.
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ژورنال
عنوان ژورنال: Physical Review D
سال: 1995
ISSN: 0556-2821
DOI: 10.1103/physrevd.52.6789