I'm trying to understand how to apply the generalized Rice's theorem to prove that a problem is Turing-Recognizable.
Suppose that I have two TMs and I have to evaluate if there exists a string that both are able to accept.
Is this problem Turing-Recognizable?
Source of the theorem: https://cs.stackexchange.com/q/2322.
The problem is Turing-Recognizable because all the hyphotesis of the theorem hold.
$w$ = common string
1) $L1=w, L2=w$ then $L2 \in RE$
2) $L1=w, L2=w$ then $L2 \in RE$
3) $w$ is a finite language