Singular Failures of GCH and Level by Level Equivalence

Arthur W. Apter. "Singular Failures of GCH and Level by Level Equivalence." Bulletin of the Polish Academy of Sciences. Mathematics 62.1 (2014): 11-21. <http://eudml.org/doc/281233>.

@article{ArthurW2014,
abstract = {We construct a model for the level by level equivalence between strong compactness and supercompactness in which below the least supercompact cardinal κ, there is an unbounded set of singular cardinals which witness the only failures of GCH in the universe. In this model, the structure of the class of supercompact cardinals can be arbitrary.},
author = {Arthur W. Apter},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {supercompact cardinal; strongly compact cardinal; strong cardinal; gitik iteration; $\kappa $-weakly closed partial ordering satisfying the prikry condition; level by level equivalence between strong compactness and supercompactness},
language = {eng},
number = {1},
pages = {11-21},
title = {Singular Failures of GCH and Level by Level Equivalence},
url = {http://eudml.org/doc/281233},
volume = {62},
year = {2014},
}

TY - JOUR
AU - Arthur W. Apter
TI - Singular Failures of GCH and Level by Level Equivalence
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2014
VL - 62
IS - 1
SP - 11
EP - 21
AB - We construct a model for the level by level equivalence between strong compactness and supercompactness in which below the least supercompact cardinal κ, there is an unbounded set of singular cardinals which witness the only failures of GCH in the universe. In this model, the structure of the class of supercompact cardinals can be arbitrary.
LA - eng
KW - supercompact cardinal; strongly compact cardinal; strong cardinal; gitik iteration; $\kappa $-weakly closed partial ordering satisfying the prikry condition; level by level equivalence between strong compactness and supercompactness
UR - http://eudml.org/doc/281233
ER -