Indestructibility, strong compactness, and level by level equivalence

• Autorzy: Arthur W. Apter
• Języki publikacji: EN

Abstrakty

EN

We show the relative consistency of the existence of two strongly compact cardinals κ₁ and κ₂ which exhibit indestructibility properties for their strong compactness, together with level by level equivalence between strong compactness and supercompactness holding at all measurable cardinals except for κ₁. In the model constructed, κ₁'s strong compactness is indestructible under arbitrary κ₁-directed closed forcing, κ₁ is a limit of measurable cardinals, κ₂'s strong compactness is indestructible under κ₂-directed closed forcing which is also (κ₂,∞)-distributive, and κ₂ is fully supercompact.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 204
• Numer: 2
• Strony: 113-126

Daty

wydano

2009

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.

Identyfikatory

DOI

10.4064/fm204-2-2