My understanding has always been that an axiomatic system requires certain undefined terms, called primitives, upon which the system’s defined terms and axioms are built. The point, obviously, is to avoid circular definitions.
For arithmetic, “successor” is undefined. (Successor is a term used to state the Induction Axiom). For geometry, “point” is undefined. And for systems of 2-logic, both “true” and “false” are undefined.
Does there in fact exist a deductive system that has no undefined terms and no circular definitions?