On level by level equivalence and inequivalence between strong compactness and supercompactness

Arthur W. Apter. "On level by level equivalence and inequivalence between strong compactness and supercompactness." Fundamenta Mathematicae 171.1 (2002): 77-92. <http://eudml.org/doc/282873>.

@article{ArthurW2002,
abstract = {We prove two theorems, one concerning level by level inequivalence between strong compactness and supercompactness, and one concerning level by level equivalence between strong compactness and supercompactness. We first show that in a universe containing a supercompact cardinal but of restricted size, it is possible to control precisely the difference between the degree of strong compactness and supercompactness that any measurable cardinal exhibits. We then show that in an unrestricted size universe containing many supercompact cardinals, it is possible to have significant failures of GCH along with level by level equivalence between strong compactness and supercompactness, except possibly at inaccessible levels.},
author = {Arthur W. Apter},
journal = {Fundamenta Mathematicae},
keywords = {supercompact cardinal; strongly compact cardinal; non-reflecting stationary set of ordinals; level by level equivalence; level by level inequivalence},
language = {eng},
number = {1},
pages = {77-92},
title = {On level by level equivalence and inequivalence between strong compactness and supercompactness},
url = {http://eudml.org/doc/282873},
volume = {171},
year = {2002},
}

TY - JOUR
AU - Arthur W. Apter
TI - On level by level equivalence and inequivalence between strong compactness and supercompactness
JO - Fundamenta Mathematicae
PY - 2002
VL - 171
IS - 1
SP - 77
EP - 92
AB - We prove two theorems, one concerning level by level inequivalence between strong compactness and supercompactness, and one concerning level by level equivalence between strong compactness and supercompactness. We first show that in a universe containing a supercompact cardinal but of restricted size, it is possible to control precisely the difference between the degree of strong compactness and supercompactness that any measurable cardinal exhibits. We then show that in an unrestricted size universe containing many supercompact cardinals, it is possible to have significant failures of GCH along with level by level equivalence between strong compactness and supercompactness, except possibly at inaccessible levels.
LA - eng
KW - supercompact cardinal; strongly compact cardinal; non-reflecting stationary set of ordinals; level by level equivalence; level by level inequivalence
UR - http://eudml.org/doc/282873
ER -