completeness

Short definition from Wiktionary

Noun

1. 1
   The state or condition of being complete.
2. 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 is true, then T⊢ϕ must also be true, for any wff φ of logic L.