Classical logic is the strongest consistent logical system

Question

I vaguely remember reading somewhere about a theorem which states that classical logic is the strongest logical system in some sense.

Unfortunately, after much search, I cannot find any reference. I’m not sure what notion of "strength" was involved here - perhaps something along the lines of "classical logic proves the greatest number of tautologies", or something similar.

I’m not even sure whether this concerned sentential or predicate logics specifically, or some other larger class.

Can anyone provide a reference to anything similar?

Answer 1

You are probably thinking of Lindstrom's theorem which says that, among a family of abstract logics, first-order logic is the strongest that satisfies the compactness theorem and the downward Lowenheim-Skolem theorem.

Answer 2

I guess you are referring to the notion of Post-completeness (also known as maximal consistency): a formal system is Post-complete if and only if it is consistent and has no consistent proper extension (i.e. no unprovable sentence can be added to it without introducing an inconsistency). On Wikipedia this property is also called syntactical completeness.

Propositional classical logic is Post-complete. First-order classical logic and propositional intuitionistic logic are not Post-complete.

For some references, you can have a look here and here (and at their bibliography).