A complete axiomatic theory is an axiomatic theory (such as a geometry) such that each valid statement in the theory is capable of being proven true or false.
Complete Axiomatic Theory
See also
ConsistencyExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Complete Axiomatic Theory." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CompleteAxiomaticTheory.html