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My question is about a variant of the usual notion of relative constructibility, $\le_c$ (which an earlier version of this question confusingly denoted "$\le_L$"), in set theory. Fix a ...

Suppose that $\phi(x)$ is a $\Delta^{1}_{2}$-formula (without parameters) and let $A:=\{x\subseteq\omega:\phi(x)\}$. It is clear that, e.g. if there are Cohen-generics over $L$, then $A$ cannot be the ...

I am wondering who proved the following fact: ($\ast$) If $\omega_1$ is not inaccessible in $L$, then there is an uncountable coanalytic set of reals without a perfect subset. I have been unable to ...