completeness

completeness englannista suomeksi

1. täydellisyys

0. Substantiivi

1. täydellisyys, valmius

completeness englanniksi

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 \vDash \phi is true, then T \vdash \phi must also be true, for any wff ''φ'' of logic ''L''.

3. (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) (..)