completeness
Etymology Noun
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Etymology Noun
completeness (uncountable)
- The state or condition of being complete.
- (logic) 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.
- 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) […]
- THEOREM 37°. (Gödel's completeness theorem 1930.) In the predicate calculus H:
- (state of being complete) completion, fulfillment; see also Thesaurus:completion
- incompleteness, unfinishedness; see also Thesaurus:incompletion
- French: complétude
- German: Vollständigkeit
- Italian: completezza
- Portuguese: completidão, completude
- Russian: полнота́
- Spanish: completitud
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.003