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A generalized Kleene-Moschovakis theorem

Authors: Leo Harrington, Lefteris Kirousis and John Schlipf
Journal: Proc. Amer. Math. Soc. 68 (1978), 209-213
MSC: Primary 02F27
MathSciNet review: 0476457
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Abstract: Moschovakis generalized a theorem of Kleene to prove that if $ \mathfrak{X}$ is a collection of subsets of any acceptable structure $ \mathfrak{M}$ such that $ (\mathfrak{M},\mathfrak{X}) \vDash \Delta _1^1$ comprehension, every hyperelementary subset of $ \mathfrak{M}$ is in $ \mathfrak{X}$. We prove an analogous result for arbitrary $ \mathfrak{M}$. We also get analogous results for $ \mathfrak{M}$ with an extra quantifier Q.

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Keywords: Admissible set, weakly Q-admissible set, strongly Q-admissible set, hyperelementary, Q-hyperelementary, deterministic-Q-hyperelementary, $ \Delta _1^1$ comprehension, nonacceptable structure
Article copyright: © Copyright 1978 American Mathematical Society

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