Consistency results concerning supercompactness

Author:
Telis K. Menas

Journal:
Trans. Amer. Math. Soc. **223** (1976), 61-91

MSC:
Primary 02K35; Secondary 02H13, 02K05

DOI:
https://doi.org/10.1090/S0002-9947-1976-0540771-8

MathSciNet review:
0540771

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Abstract: A general framework for proving relative consistency results with regard to supercompactness is developed. Within this framework we prove the relative consistency of the assertion that every set is ordinal definable with the statement asserting the existence of a supercompact cardinal. We also generalize Easton's theorem; the new element in our result is that our forcing conditions preserve supercompactness.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1976-0540771-8

Keywords:
Large cardinals,
backward Easton forcing,
ordinal definability,
supercompactness

Article copyright:
© Copyright 1976
American Mathematical Society