Axiomatizable Theory: Proving T is Axiomatizable

[Dragonfall]

Homework Statement

Suppose T is recursively enumerable. Show that T is actually axiomatizable (there is a recursive set P such that Theory of P = T).

The Attempt at a Solution

The converse of the question is easy to show, by using compactness. But I have no idea how to do this one.

 

[Dragonfall]

Anyone?