more from Herbert B. Enderton

### Single Idea 9997

#### [catalogued under 5. Theory of Logic / K. Features of Logics / 8. Enumerability]

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.