# Language containing all unambiguous grammars

Suppose $$L$$ is the language of the unambiguous grammars. That is, a sentence $$w\in{}L$$ if it is a string that describes an unambiguous context-free grammar.

Considering that deciding whether a context-free grammar is ambiguous is non-decidable, would it be correct to say that $$L$$ exists but is not recursively enumerable?

The language $$L$$ clearly exists — you just defined it!