# completeness

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## Енглески

### Именица

completeness (usually uncountable, plural completenesses)

1. the state or condition of being complete
2. (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 '"`UNIQ--postMath-00000001-QINU`"' is true, then '"`UNIQ--postMath-00000002-QINU`"' must also be true, for any wff φ of logic L.
• Lua грешка in Модул:quote at line 165: The first parameter (language code) is missing..
THEOREM 37°. (Gödel's completeness theorem 1930.) In the predicate calculus H:
(a) If ${\displaystyle \vDash F}$ [or even if ${\displaystyle \aleph _{0}}$-${\displaystyle \vDash F}$], then ${\displaystyle \vdash F}$. If ${\displaystyle E_{1},...,E_{k}\vDash F}$ [or even if ${\displaystyle E_{1},...,E_{k}\ \aleph _{0}}$-${\displaystyle \vDash F}$], then ${\displaystyle E_{1},...,E_{k}\vdash F}$.
(b) [...]