It is often said that special relativity is more general than Newtonian mechanics. Is there any precise meaning of what is meant by more "general"?
I would consider a theory A more general than a theory B if the axioms of B can be considered theorems of A. Is that a proper definition?
Consider special relativity vs Newtonian mechanics. We can state that:
For speeds below c, Newtonian mechanics hold.
But this means that Newton's axioms hold, which isn't the case, since the theorem "Newtonian mechanics hold" (i.e. its axioms are true) doesn't hold.
If we had constraint Newtonian mechanics to describe motion for speeds below c, then we could consider special relative as more general (based on the above definition).
Is there a precise meaning of what a more general theory means in physics?