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

Cummings, James

doi:10.1090/S0002-9947-1992-1041044-9

A model in which GCH holds at successors but fails at limits
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Trans. Amer. Math. Soc. 329 (1992), 1-39 Request permission

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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Unpublished notes on reverse Easton forcing