Axiomatization

Discussion of axiomatic systems

In mathematics, axiomatization is the process of taking a body of knowledge and working backwards towards its axioms. It is the formulation of a system of statements (i.e. axioms) that relate a number of primitive terms — in order that a consistent body of propositions may be derived deductively from these statements. Thereafter, the proof of any proposition should be, in principle, traceable back to these axioms. Axiomatization typically involves choices, and once a theory is axiomatic, it may be possible to change the set of axioms without affecting the mathematical results implied.