Strong compactness, measurability, and the class of supercompact cardinals

Arthur W. Apter. "Strong compactness, measurability, and the class of supercompact cardinals." Fundamenta Mathematicae 167.1 (2001): 65-78. <http://eudml.org/doc/281865>.

@article{ArthurW2001,
abstract = {We prove two theorems concerning strong compactness, measurability, and the class of supercompact cardinals. We begin by showing, relative to the appropriate hypotheses, that it is consistent non-trivially for every supercompact cardinal to be the limit of (non-supercompact) strongly compact cardinals. We then show, relative to the existence of a non-trivial (proper or improper) class of supercompact cardinals, that it is possible to have a model with the same class of supercompact cardinals in which every measurable cardinal δ is $2^\{δ\}$ strongly compact.},
author = {Arthur W. Apter},
journal = {Fundamenta Mathematicae},
keywords = {supercompact cardinal; strongly compact cardinal; nonreflecting stationary set of ordinals; consistency},
language = {eng},
number = {1},
pages = {65-78},
title = {Strong compactness, measurability, and the class of supercompact cardinals},
url = {http://eudml.org/doc/281865},
volume = {167},
year = {2001},
}

TY - JOUR
AU - Arthur W. Apter
TI - Strong compactness, measurability, and the class of supercompact cardinals
JO - Fundamenta Mathematicae
PY - 2001
VL - 167
IS - 1
SP - 65
EP - 78
AB - We prove two theorems concerning strong compactness, measurability, and the class of supercompact cardinals. We begin by showing, relative to the appropriate hypotheses, that it is consistent non-trivially for every supercompact cardinal to be the limit of (non-supercompact) strongly compact cardinals. We then show, relative to the existence of a non-trivial (proper or improper) class of supercompact cardinals, that it is possible to have a model with the same class of supercompact cardinals in which every measurable cardinal δ is $2^{δ}$ strongly compact.
LA - eng
KW - supercompact cardinal; strongly compact cardinal; nonreflecting stationary set of ordinals; consistency
UR - http://eudml.org/doc/281865
ER -