Of course there is. A language is just a subset of the power set of some symbol alphabet. So, for example, the set of all halting TMs (encoded appropriately) forms a language.
It is not a power set. A language is a subset of the word monoid generated by the alphabet by applying reccurent production of the alphabet (the star operation).
Is there a known proof that one needs at least a TM to recognize all decidable languages?
Here's my working definition of "decidable language":
A language L is decidable for some class of automata C if there is an automaton in C which recognises L and halts for all inputs.
I always thought in a similar fashion. But literature insists that the decidability is always measured with respect to a Turing Machine. Thus, I was unable to communicate to many other people on the usenet.