Level by Level Inequivalence, Strong Compactness, and GCH

Arthur W. Apter

Bulletin of the Polish Academy of Sciences. Mathematics (2012)

  • Volume: 60, Issue: 3, page 201-209
  • ISSN: 0239-7269

Abstract

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We construct three models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In the first two models, below the supercompact cardinal κ, there is a non-supercompact strongly compact cardinal. In the last model, any suitably defined ground model Easton function is realized.

How to cite

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Arthur W. Apter. "Level by Level Inequivalence, Strong Compactness, and GCH." Bulletin of the Polish Academy of Sciences. Mathematics 60.3 (2012): 201-209. <http://eudml.org/doc/281131>.

@article{ArthurW2012,
abstract = {We construct three models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In the first two models, below the supercompact cardinal κ, there is a non-supercompact strongly compact cardinal. In the last model, any suitably defined ground model Easton function is realized.},
author = {Arthur W. Apter},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {supercompact cardinal; strongly compact cardinal; level-by-level inequivalence between strong compactness and supercompactness; non-reflecting stationary set of ordinals; Easton function; Magidor iteration of Prikry forcing},
language = {eng},
number = {3},
pages = {201-209},
title = {Level by Level Inequivalence, Strong Compactness, and GCH},
url = {http://eudml.org/doc/281131},
volume = {60},
year = {2012},
}

TY - JOUR
AU - Arthur W. Apter
TI - Level by Level Inequivalence, Strong Compactness, and GCH
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2012
VL - 60
IS - 3
SP - 201
EP - 209
AB - We construct three models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In the first two models, below the supercompact cardinal κ, there is a non-supercompact strongly compact cardinal. In the last model, any suitably defined ground model Easton function is realized.
LA - eng
KW - supercompact cardinal; strongly compact cardinal; level-by-level inequivalence between strong compactness and supercompactness; non-reflecting stationary set of ordinals; Easton function; Magidor iteration of Prikry forcing
UR - http://eudml.org/doc/281131
ER -

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