Characterising subsets of ω1 constructible from a real

Journal of Symbolic Logic 59 (4):1420 - 1432 (1994)
A small large cardinal upper bound in V for proving when certain subsets of ω 1 (including the universally Baire subsets) are precisely those constructible from a real is given. In the core model we find an exact equivalence in terms of the length of the mouse order; we show that $\forall B \subseteq \omega_1 \lbrack B$ is universally Baire $\Leftrightarrow B \in L\lbrack r \rbrack$ for some real r] is preserved under set-sized forcing extensions if and only if there are arbitrarily large "admissibly measurable" cardinals
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DOI 10.2307/2275715
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