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 ?