completeness
nounEtymology From complete + -ness.
1
Usually The state or condition of being complete.
2
Human sciences, Logic, Mathematics, Philosophy, Sciences Usually 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⊨ϕ is true, then T⊢ϕ 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 #92;vDashF [or even if #92;aleph#95;0-#92;vDashF], then #92;vdashF. If E#95;1,...,E#95;k#92;vDashF [or even if E#95;1,...,E#95;k#92;#92;aleph#95;0-#92;vDashF], then E#95;1,...,E#95;k#92;vdashF. (b) […]2002, Stephen Cole Kleene, Mathematical Logic, Mineola, New York: Dover Publications, →ISBN, page 314:
- Synonyms
- completion, fulfillment
- Antonyms
- incompleteness, unfinishedness
- Derived terms
- completeness axiom