Uncountable admissibles. I. Forcing
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 Trans. Amer. Math. Soc. 270 (1982), 6173 Request permission
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 $\kappa = \omega$.References

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Additional Information
 © Copyright 1982 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 270 (1982), 6173
 MSC: Primary 03D60; Secondary 03C70, 03E45
 DOI: https://doi.org/10.1090/S00029947198206423308
 MathSciNet review: 642330