On the consistency strength of the inner model hypothesis
نویسندگان
چکیده
منابع مشابه
On the consistency strength of the inner model hypothesis
We repeat the statement of the IMH, as presented in [5]. A sentence in the language of set theory is internally consistent iff it holds in some (not necessarily proper) inner model. The meaning of internal consistency depends on what inner models exist: If we enlarge the universe, it is possible that more statements become internally consistent. The Inner Model Hypothesis asserts that the unive...
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Internal Consistency and the Inner Model Hypothesis
Assume that the universe V of all sets is rich in the sense that it contains inner models with large cardinals. Then what is the relationship between Easton’s model L[G] and V ? In particular, are these models compatible, in the sense that they are inner models of a common third model? If not, then the failure of GCH at every regular cardinal is consistent only in a weak sense, as it can only h...
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2008
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1208359050