The state or condition of being complete.

(logic) The property of a logical theory that whenever a wff is valid then it must also be a theorem. Symbolically, letting T represent a theory within logic L, this can be represented as the property that whenever T ⊨ ϕ {\displaystyle T\vDash \phi } is true, then T ⊢ ϕ {\displaystyle T\vdash \phi } must also be true, for any wff φ of logic L.