# Strong compactness, measurability, and the class of supercompact cardinals

Fundamenta Mathematicae (2001)

- Volume: 167, Issue: 1, page 65-78
- ISSN: 0016-2736

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topArthur 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 -

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