more from Herbert B. Enderton

### Single Idea 9720

#### [catalogued under 5. Theory of Logic / K. Features of Logics / 4. Completeness]

Full Idea

If every semantically valid inference is proof-theoretically valid (so that |= entails |-), the proof-theory is said to be 'complete'.

Gist of Idea

A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity

Source

Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.7)

Book Reference

Enderton,Herbert B.: 'A Mathematical Introduction to Logic' [Academic Press 2001], p.2