completeness — Dizionario inglese

Sostantivo

1. The state or condition of being complete.

   Uso

   • non numerabile
   • usually

2. 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.

   Uso

   • non numerabile
   • usually

   Esempi

   Altri esempi (1)

   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) […]

Sostantivo

1. the state of being complete and entire; having everything that is needed

   Contrari

   incompleteness

   Termini più generali

   integrityunitywholeness

2. (logic) an attribute of a logical system that is so constituted that a contradiction arises if any proposition is introduced that cannot be derived from the axioms of the system

   Termini più generali

   logicalitylogicalness