Full Idea
The Enumerability Theorem says that for a reasonable language, the set of valid wff's can be effectively enumerated.
Clarification
a 'wff' is a well-formed formula
Gist of Idea
For a reasonable language, the set of valid wff's can always be enumerated
Source
Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 2.5)
Book Reference
Enderton,Herbert B.: 'A Mathematical Introduction to Logic' [Academic Press 2001], p.142
A Reaction
There are criteria for what makes a 'reasonable' language (probably specified to ensure enumerability!). Predicates and functions must be decidable, and the language must be finite.