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A model in which GCH holds at successors but fails at limits


Author: James Cummings
Journal: Trans. Amer. Math. Soc. 329 (1992), 1-39
MSC: Primary 03E35; Secondary 03E50, 03E55
DOI: https://doi.org/10.1090/S0002-9947-1992-1041044-9
MathSciNet review: 1041044
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Abstract: Starting with GCH and a $ {\mathcal{P}_3}\kappa $-hypermeasurable cardinal, a model is produced in which $ {2^\lambda } = {\lambda ^ + }$ if $ \lambda $ is a successor cardinal and $ {2^\lambda } = {\lambda ^{ + + }}$ if $ \lambda $ is a limit cardinal. The proof uses a Reverse Easton extension followed by a modified Radin forcing.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1041044-9
Keywords: Radin forcing, singular cardinals problem, large cardinals
Article copyright: © Copyright 1992 American Mathematical Society

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