Determinacy in strong cardinal models
نویسندگان
چکیده
منابع مشابه
Determinacy in strong cardinal models
We give limits defined in terms of abstract pointclasses of the amount of determinacy available in certain canonical inner models involving strong cardinals. We show for example: Theorem A Det(Π1-IND)⇒there exists an inner model with a strong cardinal. Theorem B Det(AQI)⇒there exist type-1 mice and hence inner models with proper classes of strong cardinals where Π1-IND (AQI) is the pointclass o...
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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...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2011
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1305810772