Propositional Logic Part 8: Completeness and Compactness

In this video we prove the Completeness Theorem, which states that a set of sentences is consistent exactly when they have a model. We also prove the compactness theorem, which states that a set of sentences has a model if and only if every finite subset has a model.

Apologies for the section at 10:50, there is a much, much easier approach. Rewrite the implication as "not ( psi_k and not psi_i)." Now, we conclude that A cannot model "not psi_i" directly from the recursive definition of truth in a model.

0:00 Statement of the Extended Completeness Theorem
3:53 Proof that satisfiable implies consistent
5:01 Proof of a lemma
12:58 Conclusion of the proof
16:46 Proof that consistent implies satisfiable
20:20 Maximal consistent theories are closed under deduction
23:07 Inductive proof that our model satisfies
30:57 Proof of the Compactness Theorem
37:33 Conclusion of Propositional Logic
39:54 Motivation for Predicate Logic
42:59 Final note on what's to follow