Level by level equivalence and the number of normal measures over $P_{\kappa }\left(\lambda \right)$

Arthur W. Apter. "Level by level equivalence and the number of normal measures over $P_{κ}(λ)$." Fundamenta Mathematicae 194.3 (2007): 253-265. <http://eudml.org/doc/283233>.

@article{ArthurW2007,
abstract = {We construct two models for the level by level equivalence between strong compactness and supercompactness in which if κ is λ supercompact and λ ≥ κ is regular, we are able to determine exactly the number of normal measures $P_\{κ\}(λ)$ carries. In the first of these models, $P_\{κ\}(λ)$ carries $2^\{2^\{[λ]^\{<κ\}\}\}$ many normal measures, the maximal number. In the second of these models, $P_\{κ\}(λ)$ carries $2^\{2^\{[λ]^\{<κ\}\}\}$ many normal measures, except if κ is a measurable cardinal which is not a limit of measurable cardinals. In this case, κ (and hence also $P_\{κ\}(κ)$) carries only κ⁺ many normal measures. In both of these models, there are no restrictions on the structure of the class of supercompact cardinals.},
author = {Arthur W. Apter},
journal = {Fundamenta Mathematicae},
keywords = {supercompact cardinal; strongly compact cardinal; normal measure; level by level equivalence between strong compactness and supercompactness},
language = {eng},
number = {3},
pages = {253-265},
title = {Level by level equivalence and the number of normal measures over $P_\{κ\}(λ)$},
url = {http://eudml.org/doc/283233},
volume = {194},
year = {2007},
}

TY - JOUR
AU - Arthur W. Apter
TI - Level by level equivalence and the number of normal measures over $P_{κ}(λ)$
JO - Fundamenta Mathematicae
PY - 2007
VL - 194
IS - 3
SP - 253
EP - 265
AB - We construct two models for the level by level equivalence between strong compactness and supercompactness in which if κ is λ supercompact and λ ≥ κ is regular, we are able to determine exactly the number of normal measures $P_{κ}(λ)$ carries. In the first of these models, $P_{κ}(λ)$ carries $2^{2^{[λ]^{<κ}}}$ many normal measures, the maximal number. In the second of these models, $P_{κ}(λ)$ carries $2^{2^{[λ]^{<κ}}}$ many normal measures, except if κ is a measurable cardinal which is not a limit of measurable cardinals. In this case, κ (and hence also $P_{κ}(κ)$) carries only κ⁺ many normal measures. In both of these models, there are no restrictions on the structure of the class of supercompact cardinals.
LA - eng
KW - supercompact cardinal; strongly compact cardinal; normal measure; level by level equivalence between strong compactness and supercompactness
UR - http://eudml.org/doc/283233
ER -