Indestructibility, HOD, and the Ground Axiom
نویسندگان
چکیده
منابع مشابه
Indestructibility, HOD, and the Ground Axiom
Let φ1 stand for the statement V = HOD and φ2 stand for the Ground Axiom. Suppose Ti for i = 1, . . . , 4 are the theories “ZFC + φ1 + φ2”, “ZFC + ¬φ1 + φ2”, “ZFC + φ1 + ¬φ2”, and “ZFC + ¬φ1 + ¬φ2” respectively. We show that if κ is indestructibly supercompact and λ > κ is inaccessible, then for i = 1, . . . , 4, Ai =df {δ < κ | δ is an inaccessible cardinal which is not a limit of inaccessible...
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In an attempt to extend the property of being supercompact but not hod-supercompact to a proper class of indestructibly supercompact cardinals, a theorem is discovered about a proper class of indestructibly supercompact cardinals which reveals a surprising incompatibility. However, it is still possible to force to get a model in which the property of being supercompact but not hod-supercompact ...
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I present a forcing indestructibility theorem for the large cardinal axiom Vopěnka’s Principle. It is notable in that there is no preparatory forcing required to make the axiom indestructible, unlike the case for other indestructibility results. §
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ژورنال
عنوان ژورنال: Mathematical Logic Quarterly
سال: 2011
ISSN: 0942-5616
DOI: 10.1002/malq.201010005