I am trying to sharpen the line among the definitions of tautology, axiom and premise.
What I have understood so far is this:
Tautology: A statement that is proven to be true without relying on any axiom.
Axiom: A statement that is assumed to be true without a proof or by proof using at least one axiom.
Premise: A statement that is assumed to be true to get a conclusive statement. So it has a scope different from that of an axiom.
Are these correct, and if not what would be the way to describe them?