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complete +‎ -ness

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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   is true, then   must also be true, for any wff φ of logic L.
    • 2002, Stephen Cole Kleene, Mathematical Logic, Mineola, New York: Dover Publications, →ISBN, page 314:
      THEOREM 37°. (Gödel's completeness theorem 1930.) In the predicate calculus H:
      (a) If   [or even if  - ], then  . If   [or even if  - ], then  .
      (b) []

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