HOD-supercompactness, Indestructibility, and Level by Level Equivalence

• Autorzy: Arthur W. Apter , Shoshana Friedman
• Języki publikacji: EN

Abstrakty

EN

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 holds for the least supercompact cardinal κ₀, κ₀ is indestructibly supercompact, the strongly compact and supercompact cardinals coincide except at measurable limit points, and level by level equivalence between strong compactness and supercompactness holds above κ₀ but fails below κ₀. Additionally, we get the property of being supercompact but not HOD-supercompact at the least supercompact cardinal, in a model where level by level equivalence between strong compactness and supercompactness holds.

Kategorie tematyczne

• 03E55: Large cardinals
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: 62
• Numer: 3
• Strony: 197-209

Daty

wydano

2014

Twórcy

autor

Arthur W. Apter

• Department of Mathematics, Baruch College of CUNY, New York, NY 10010, U.S.A.
• The CUNY Graduate Center, Mathematics, 365 Fifth Avenue, New York, NY 10016, U.S.A.

autor

Shoshana Friedman

• Department of Mathematics and Computer Science, Kingsborough Community College-CUNY, 2001 Oriental Blvd, Brooklyn, NY 11235, U.S.A.

Identyfikatory

DOI

10.4064/ba62-3-1