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Uncountable Admissibles I: Forcing

Sy D. Friedman
Transactions of the American Mathematical Society
Vol. 270, No. 1 (Mar., 1982), pp. 61-73
DOI: 10.2307/1999761
Stable URL: http://www.jstor.org/stable/1999761
Page Count: 13
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Uncountable Admissibles I: Forcing
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Abstract

Assume V = L. Let κ be a regular cardinal and for $X \subseteq \kappa$ let α(X) denote the least ordinal α such that Lα[ X ] is admissible. In this paper we characterize those ordinals of the form α(X) using forcing and fine structure of L techniques. This generalizes a theorem of Sacks which deals with the case κ = ω.

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