A Generalized Kleene-Moschovakis Theorem
A Generalized Kleene-Moschovakis Theorem
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 …