# Whether language of all turing machines is decidable or undecidable or semi-decidable?

I recently came across this language:

$$L=\{| \text{TM accepts recursively enumerable languages}\}$$

It was asked in the question to find out whether language L is decidable or undecidable.

As far as I could reason out, language L is the set of all recursive enumerable languages or set of all turing machines.

But I can't figure out whether this language is decidable or not.

Can anyone please help me out??

Thanks in advance!!

• Well, if, as you say, $L$ is simply the language of all TM encodings, then what do you need to check in order to decide it? – dkaeae Dec 4 '18 at 9:10