completeness of first-order logic


Godel's Completeness Theorem shows that there is a complete (and sound) deductive calculus for first-order logic. In other words, if some set of sentences is consistent (one cannot derive a contradiction from them), then there is some model in which all the sentences are satisfied. This result is significant in that it unifies the syntax and semantics of first-order logic.


This concept has the prerequisites:


  • Know what it means for a first-order deductive calculus to be complete
  • Know the statement of Godel's Completeness Theorem
  • Prove Godel's Completeness Theorem (Henkin's proof in particular)
  • Using the Completeness Theorem, prove the Compactness Theorem for first-order logic.

Core resources (read/watch one of the following)


Notes on Logic (2013)


See also

-No Additional Notes-