Everyone knows that Kurt Gödel gave the first proof of the Completeness Theorem for first-order logic in his 1929 doctoral dissertation Über die Vollständigkeit des Logikkalküls, with subsequent important refinements by Henkin and others.

But what about the completeness and compactness of propositional logic? Does it have an earlier proof?

König's Lemma (1927) predates Gödel's proof, and is equivalent to compactness of propositional logic, but I don't know if anyone was aware of this at the time.


1 Answer 1


Completeness: Emil Post: Introduction to a General Theory of Elementary Propositions (1921), and Paul Bernays (1918).

For compacteness, I think that it was a by-product of the FOL version; for sure, it was explicitly generalized to the uncountable case by Anatoly Malcev : Investigations in the realm of mathematical logic [Untersuchungen aus dem Gebiete der mathematischen Logik] (1936).


You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .