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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Uncountable admissibles. I. Forcing


Author: Sy D. Friedman
Journal: Trans. Amer. Math. Soc. 270 (1982), 61-73
MSC: Primary 03D60; Secondary 03C70, 03E45
MathSciNet review: 642330
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Abstract: Assume $ V = L$. Let $ \kappa $ be a regular cardinal and for $ X \subseteq \kappa $ let $ \alpha (X)$ denote the least ordinal $ \alpha $ such that $ {L_\alpha }[X]$ is admissible. In this paper we characterize those ordinals of the form $ \alpha (X)$ using forcing and fine structure of $ L$ techniques. This generalizes a theorem of Sacks which deals with the case $ \kappa = \omega $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0642330-8
PII: S 0002-9947(1982)0642330-8
Article copyright: © Copyright 1982 American Mathematical Society