Mixed Levels of Indestructibility

Arthur W. Apter

Bulletin of the Polish Academy of Sciences. Mathematics (2015)

  • Volume: 63, Issue: 2, page 113-122
  • ISSN: 0239-7269

Abstract

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Starting from a supercompact cardinal κ, we force and construct a model in which κ is both the least strongly compact and least supercompact cardinal and κ exhibits mixed levels of indestructibility. Specifically, κ 's strong compactness, but not its supercompactness, is indestructible under any κ -directed closed forcing which also adds a Cohen subset of κ. On the other hand, in this model, κ 's supercompactness is indestructible under any κ -directed closed forcing which does not add a Cohen subset of κ.

How to cite

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Arthur W. Apter. "Mixed Levels of Indestructibility." Bulletin of the Polish Academy of Sciences. Mathematics 63.2 (2015): 113-122. <http://eudml.org/doc/281304>.

@article{ArthurW2015,
abstract = {Starting from a supercompact cardinal κ, we force and construct a model in which κ is both the least strongly compact and least supercompact cardinal and κ exhibits mixed levels of indestructibility. Specifically, κ 's strong compactness, but not its supercompactness, is indestructible under any κ -directed closed forcing which also adds a Cohen subset of κ. On the other hand, in this model, κ 's supercompactness is indestructible under any κ -directed closed forcing which does not add a Cohen subset of κ.},
author = {Arthur W. Apter},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {supercompact cardinal; strongly compact cardinal; strong cardinal; indestructibility; prikry forcing; prikry sequence; non-reflecting stationary set of ordinals; lottery sum},
language = {eng},
number = {2},
pages = {113-122},
title = {Mixed Levels of Indestructibility},
url = {http://eudml.org/doc/281304},
volume = {63},
year = {2015},
}

TY - JOUR
AU - Arthur W. Apter
TI - Mixed Levels of Indestructibility
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2015
VL - 63
IS - 2
SP - 113
EP - 122
AB - Starting from a supercompact cardinal κ, we force and construct a model in which κ is both the least strongly compact and least supercompact cardinal and κ exhibits mixed levels of indestructibility. Specifically, κ 's strong compactness, but not its supercompactness, is indestructible under any κ -directed closed forcing which also adds a Cohen subset of κ. On the other hand, in this model, κ 's supercompactness is indestructible under any κ -directed closed forcing which does not add a Cohen subset of κ.
LA - eng
KW - supercompact cardinal; strongly compact cardinal; strong cardinal; indestructibility; prikry forcing; prikry sequence; non-reflecting stationary set of ordinals; lottery sum
UR - http://eudml.org/doc/281304
ER -

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