completeness

täydellisyys the state or condition of being complete
puhekieltä 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 \vDash \phi is true, then T \vdash \phi must also be true, for any wff φ of logic L.
(quote-book)

THEOREM 37°. (Gödel's completeness theorem 1930.) In the predicate calculus H:(a) If \vDash F or even if \aleph_0-\vDash F, then \vdash F. If E_1, . . . , E_k \vDash F or even if E_1, . . . , E_k \ \aleph_0-\vDash F, then E_1, . . . , E_k \vdash F.(b) ...