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Precisely controlling level by level behavior
Author(s) -
Apter Arthur W.
Publication year - 2017
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.201500018
Subject(s) - mathematics , compact space , regular cardinal , equivalence (formal languages) , pure mathematics , discrete mathematics
We construct four models containing one supercompact cardinal in which level by level equivalence between strong compactness and supercompactness and level by level inequivalence between strong compactness and supercompactness are precisely controlled at each non‐supercompact measurable cardinal. In these models, no cardinal κ is < κ ′ ‐supercompact, where κ ′ is the least inaccessible cardinal greater than κ.