Collapsing the Cardinals of Hod
نویسنده
چکیده
Assuming that GCH holds and κ is κ+3-supercompact, we construct a generic extension W of V in which κ remains strongly inaccessible and (α+)HOD < α+ for every infinite cardinal α < κ. In particular the rank-initial segment Wκ is a model of ZFC in which (α+)HOD < α+ for every infinite cardinal α.
منابع مشابه
Hod, V and the GCH
Starting from large cardinals we construct a model of ZFC in which the GCH fails everywhere, but such that GCH holds in its HOD. The result answers a question of Sy Friedman. Also, relative to the existence of large cardinals, we produce a model of ZFC +GCH such that GCH fails everywhere in its HOD.
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Supercompact extender based forcings are used to construct models with HOD cardinal structure different from those of V . In particular, a model with all regular uncountable cardinals measurable in HOD is constructed.
متن کاملOn the powersets of singular cardinals in HOD
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تاریخ انتشار 2015