The Completeness Theorem finishes our link between deducibility and logical implication. The Compactness Theorem is our first use of that link. In some sense, what the Compactness Theorem does is focu...The Completeness Theorem finishes our link between deducibility and logical implication. The Compactness Theorem is our first use of that link. In some sense, what the Compactness Theorem does is focus our attention on the finiteness of deductions, and then we can begin to use that finiteness to our advantage.
