Is it decidable when a TM M gets another as inputs and checks if it fullfiills certain property? I was asking myself if it is not possible to decide the language where a TM M gets the Godel number of a TM M' as input and the checks if, let us say, the TM M' has a certain amount of transitions.
My idea was that it is decidable because we have an countably infinite amount of Godel numbers and the number of TMs which fulfill a certain property is also countably infinite. Therefor, we could make a reduction with the Halting-problem and show via this way that it is undecidable.
That definitely isn't enough. The set of Turing machines that always halt is countable (being a subset of the countable set of all Turing machines), but very not decidable.
Don't overcomplicate: If you are given a Turing machine, any property of the machine as such (number of states, number of transitions, is it deterministic, ...) that can be checked by a deterministic algorithm is obviously decidable.