Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 03E35, 03E50, 03E55

Retrieve articles in all journals with MSC: 03E35, 03E50, 03E55


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