Abstract
We show that the theories “ZFC \(+\) There is a supercompact cardinal” and “ZFC \(+\) There is a supercompact cardinal \(+\) Level by level inequivalence between strong compactness and supercompactness holds” are equiconsistent.
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This paper is dedicated to the memory of Jim Baumgartner, a friend and inspiration to all those who knew him.
The author’s research was partially supported by PSC-CUNY Grants. The author wishes to thank Norman Perlmutter for a helpful conversation on the subject matter of this paper.
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Apter, A.W. On the consistency strength of level by level inequivalence. Arch. Math. Logic 56, 715–723 (2017). https://doi.org/10.1007/s00153-017-0538-7
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DOI: https://doi.org/10.1007/s00153-017-0538-7
Keywords
- Supercompact cardinal
- Strongly compact cardinal
- Level by level inequivalence between strong compactness and supercompactness
- Nonreflecting stationary set of ordinals
- Equiconsistency