A consistency proof for a formal theory establishes that the theory cannot derive a contradiction. Relative consistency proves that consistency of one theory implies consistency of another, while a model proves consistency when the background metatheory can verify that all axioms hold in it.
Consistency Proof
See also
Axiom, Model TheoryExplore with Wolfram|Alpha
References
Kleene, S. C. Introduction to Metamathematics. Amsterdam, Netherlands: North-Holland, 1952.Cite this as:
Weisstein, Eric W. "Consistency Proof." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ConsistencyProof.html