Indestructibility, strong compactness, and level by level equivalence

Arthur W. Apter

Fundamenta Mathematicae (2009)

  • Volume: 204, Issue: 2, page 113-126
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Arthur W. Apter. "Indestructibility, strong compactness, and level by level equivalence." Fundamenta Mathematicae 204.2 (2009): 113-126. <http://eudml.org/doc/282611>.

@article{ArthurW2009,
abstract = {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.},
author = {Arthur W. Apter},
journal = {Fundamenta Mathematicae},
keywords = {supercompact cardinal; strongly compact cardinal; indestructibility; non-reflecting stationary set of ordinals; level-by-level equivalence between strong compactness and supercompactness},
language = {eng},
number = {2},
pages = {113-126},
title = {Indestructibility, strong compactness, and level by level equivalence},
url = {http://eudml.org/doc/282611},
volume = {204},
year = {2009},
}

TY - JOUR
AU - Arthur W. Apter
TI - Indestructibility, strong compactness, and level by level equivalence
JO - Fundamenta Mathematicae
PY - 2009
VL - 204
IS - 2
SP - 113
EP - 126
AB - 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.
LA - eng
KW - supercompact cardinal; strongly compact cardinal; indestructibility; non-reflecting stationary set of ordinals; level-by-level equivalence between strong compactness and supercompactness
UR - http://eudml.org/doc/282611
ER -

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