Supercompactness and partial level by level equivalence between strong compactness and strongness

Arthur W. Apter. "Supercompactness and partial level by level equivalence between strong compactness and strongness." Fundamenta Mathematicae 182.2 (2004): 123-136. <http://eudml.org/doc/283015>.

@article{ArthurW2004,
abstract = {We force and construct a model containing supercompact cardinals in which, for any measurable cardinal δ and any ordinal α below the least beth fixed point above δ, if $δ^\{+α\}$ is regular, δ is $δ^\{+α\}$ strongly compact iff δ is δ + α + 1 strong, except possibly if δ is a limit of cardinals γ which are $δ^\{+α\}$ strongly compact. The choice of the least beth fixed point above δ as our bound on α is arbitrary, and other bounds are possible.},
author = {Arthur W. Apter},
journal = {Fundamenta Mathematicae},
keywords = {supercompact cardinal; strongly compact cardinal; strong cardinal; measurable cardinal; non-reflecting stationary set of ordinals; level by level equivalence between strong compactness and supercompactness; level by level equivalence between strong compactness and strongness},
language = {eng},
number = {2},
pages = {123-136},
title = {Supercompactness and partial level by level equivalence between strong compactness and strongness},
url = {http://eudml.org/doc/283015},
volume = {182},
year = {2004},
}

TY - JOUR
AU - Arthur W. Apter
TI - Supercompactness and partial level by level equivalence between strong compactness and strongness
JO - Fundamenta Mathematicae
PY - 2004
VL - 182
IS - 2
SP - 123
EP - 136
AB - We force and construct a model containing supercompact cardinals in which, for any measurable cardinal δ and any ordinal α below the least beth fixed point above δ, if $δ^{+α}$ is regular, δ is $δ^{+α}$ strongly compact iff δ is δ + α + 1 strong, except possibly if δ is a limit of cardinals γ which are $δ^{+α}$ strongly compact. The choice of the least beth fixed point above δ as our bound on α is arbitrary, and other bounds are possible.
LA - eng
KW - supercompact cardinal; strongly compact cardinal; strong cardinal; measurable cardinal; non-reflecting stationary set of ordinals; level by level equivalence between strong compactness and supercompactness; level by level equivalence between strong compactness and strongness
UR - http://eudml.org/doc/283015
ER -