Suppose 'Fx' is a unary recursive relation. Also suppose that (∃x)Fx is a consequence of the standard model for number theory. Is the function on natural numbers f recursive that returns 0 if
Fn and, for m < n, Fm is not a consequence of the standard model
and returns 1 otherwise?
Since is recursive, one can check for each number whether and . So yes, is recursive. The assumption that is not used here.
This question is more suitable for the Discrete Mathematics, Set Theory and Logic section of the forum.