HOD-supercompactness, Indestructibility, and Level by Level Equivalence

Arthur W. Apter, and Shoshana Friedman. "HOD-supercompactness, Indestructibility, and Level by Level Equivalence." Bulletin of the Polish Academy of Sciences. Mathematics 62.3 (2014): 197-209. <http://eudml.org/doc/281251>.

@article{ArthurW2014,
abstract = {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.},
author = {Arthur W. Apter, Shoshana Friedman},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {supercompact cardinal; strongly compact cardinal; measurable cardinal; HOD; level by level equivalence between strong compactness and supercompactness},
language = {eng},
number = {3},
pages = {197-209},
title = {HOD-supercompactness, Indestructibility, and Level by Level Equivalence},
url = {http://eudml.org/doc/281251},
volume = {62},
year = {2014},
}

TY - JOUR
AU - Arthur W. Apter
AU - Shoshana Friedman
TI - HOD-supercompactness, Indestructibility, and Level by Level Equivalence
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2014
VL - 62
IS - 3
SP - 197
EP - 209
AB - 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.
LA - eng
KW - supercompact cardinal; strongly compact cardinal; measurable cardinal; HOD; level by level equivalence between strong compactness and supercompactness
UR - http://eudml.org/doc/281251
ER -