## Is $\{w~|~\forall x \in T(M_v):|w|>|x|~\}$ decidable?

I want to ask if $$\{w|\forall x\in T(M_v):|w|>|x|\}$$ is decidable if v is a Index of a random but fixed Turing Machine with $$|T(M_v)|<\infty$$.

My idea: It is co-semi-decidable since as soon as i find an $$x\in T(M_v)$$ with $$|x|\geq |w|$$ I have shown that this sepcific w is not in the set. I think it aint semi-decidable, since there can always be an $$x\in T(M_v)$$ which is longer than w. Therefor i also think the problem ist undecidable.

Do i oversee something ?