A generalized Kleene-Moschovakis theorem
Leo A. Harrington, Lefteris M. Kirousis, John Stewart Schlipf · Proceedings of the American Mathematical Society · 1978
Moschovakis generalized a theorem of Kleene to prove that if X \mathfrak {X} is a collection of subsets of any acceptable structure M \mathfrak {M} such that ( M , X ) ⊨ Δ 1 1 (\mathfrak {M},\mathfrak {X}) \vDash \Delta _1^1 comprehension, every hyperelementary subset of M \mathfrak {M} is in X \mathfrak {X} . We prove an analogous result for arbitrary M \mathfrak {M} . We also get analogous results for M \mathfrak {M} with an extra quantifier Q.