axiomatic system

An axiomatic system is any set of primitive notions and axioms to logically derive theorems.

An axiomatic system is consistent if it lacks contradiction.

An axiomatic system is complete if every proposition is capable of being proven true or false.

An axiom in an axiomatic system is independent if it cannot be proven or disproven from the other axioms in the system.

An axiomatic system with a valid interpretation is called a model.