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 $$T \vDash \phi$$ is true, then $$T \vdash \phi$$ must also be true, for any wff &phi; of logic L.
 * THEOREM 37&deg;. (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)
 * THEOREM 37&deg;. (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)

Synonyms

 * , ; see also Thesaurus:completion

Antonyms

 * , ; see also Thesaurus:incompletion

Translations

 * Bulgarian: ,
 * Chinese:
 * Mandarin:
 * Czech: úplnost
 * Esperanto: tuteco
 * Finnish: ,
 * French:
 * German:
 * Greek:
 * Ancient: ἐντέλεια
 * Hebrew: שלמות
 * Indonesian:
 * Irish: foirfeacht
 * Italian:
 * Polish: całkowitość,, ,
 * Portuguese: completidão,
 * Russian:, завершёность, зако́нченнность,
 * Spanish:
 * Swedish:
 * Turkish: