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Failures of GCH and the level by level equivalence between strong compactness and supercompactness
Author(s) -
Apter Arthur W.
Publication year - 2003
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310064
Subject(s) - mathematics , compact space , equivalence (formal languages) , pure mathematics , class (philosophy) , measure (data warehouse) , regular cardinal , set (abstract data type) , discrete mathematics , computer science , data mining , artificial intelligence , programming language
We force and obtain three models in which level by level equivalence between strong compactness and supercompactness holds and in which, below the least supercompact cardinal, GCH fails unboundedly often. In two of these models, GCH fails on a set having measure 1 with respect to certain canonical measures. There are no restrictions in all of our models on the structure of the class of supercompact cardinals. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)