English

Noun

completeness ‎(uncountable)

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 0-486-42533-9 (pbk.), 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) [...]

Synonyms

• (state of being complete): completion

Antonyms

• incompleteness

Translations