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n the state or condition of being complete

n (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 $T\; \backslash vDash\; \backslash phi$ is true, then $T\; \backslash vdash\; \backslash phi$ must also be true, for any wff φ of logic L.