Completeness

English

Alternative forms

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Etymology

From Template:Suffix.

Noun

1. The state or condition of being complete.
2. Template:Lb 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 $T\models \varphi$ is true, then $T⊢\varphi$ must also be true, for any wff φ of logic L.
   • Template:Quote-book

     THEOREM 37°. (Gödel's completeness theorem 1930.) In the predicate calculus H:
     (a) If $\models F$ [or even if ${\mathrm{\aleph }}_0$-$\models F$], then $⊢F$. If $E_1,...,E_k\models F$ [or even if $E_1,...,E_k{\mathrm{\aleph }}_0$-$\models F$], then $E_1,...,E_k⊢F$.
     (b) Template:...

Synonyms

• Template:Sense Template:L, Template:L; see also Thesaurus:completion

Antonyms

• Template:L, Template:L; see also Thesaurus:incompletion

Derived terms

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