Completeness

Noun

1. The state or condition of being complete.
2. 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<!-- ϕ --> {\displaystyle T\vDash \phi } is true, then T ⊢<!-- ⊢ --> ϕ<!-- ϕ --> {\displaystyle T\vdash \phi } must also be true, for any wff φ of logic L.