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A note on tall cardinals and level by level equivalence
Author(s) -
Apter Arthur W.
Publication year - 2016
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.201500063
Subject(s) - mathematics , regular cardinal , equivalence (formal languages) , compact space , pure mathematics , discrete mathematics , combinatorics
Starting from a model V ⊧ ZFC + GCH + “κ is supercompact” + “No cardinal is supercompact up to a measurable cardinal”, we force and construct a model V P such thatV P ⊧ ZFC + “κ is supercompact” + “No cardinal is supercompact up to a measurable cardinal” + “δ is measurable iff δ is tall” in which level by level equivalence between strong compactness and supercompactness holds. This extends and generalizes both [[4][A. Apter, 2014], Theorem 1] and the results of [5][A. Apter, 1997].