Abstract
AssumeV=L. Let κ be a cardinal and forX⊆κ, n<ω let α n (X) denote the least ordinal α such thatL α[X] is Σ n admissible. In our earlier paperUncountable admissibles I: forcing, we characterized those ordinals of the form σ n (X) when κ is regular. This paper treats the singular case using Barwise compactness, an effective version of Jensen's covering lemma and β-recursion theory.
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Friedman, S.D. Uncountable admissibles II: Compactness. Israel J. Math. 40, 129–149 (1981). https://doi.org/10.1007/BF02761905
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DOI: https://doi.org/10.1007/BF02761905