Axiomatizable Theory: Proving T is Axiomatizable

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In summary, an Axiomatizable Theory is a formal system consisting of axioms and rules that describe a mathematical or logical system and allow for the derivation of theorems within that system. To prove that a theory is Axiomatizable, one must show the ability to construct a complete set of axioms and rules. The benefits of having an Axiomatizable Theory include a clear understanding of the system, the ability to systematically derive theorems, and the potential for further research and development. However, not all theories can be proven to be Axiomatizable due to their complexity or limitations in formal proof methods. Axiomatizable Theory has applications in various branches of science, including physics and computer science.
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Dragonfall
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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.
 
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Anyone?
 

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