I am wondering, whether there a exists a recursive set $S\subseteq \mathbb{N}^2$, such that for every recursive set $T \subseteq \mathbb{N} \ \exists c \in \mathbb{N}: \ T=\left\{n \in \mathbb{N }| (c,n) \in S\right\}$ ? (And by "recursive set" I mean a set that is a projection of a recursive set; and by "recursive set" one whose characteristic function is recursive)
I know a similar proposition holds, if we replace "recursive with "recursively enumerable", but somehow I can't figure this one out...