completeness

English

Alternative forms

• completenesse (obsolete)

Etymology

complete +‎ -ness

Noun

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 $T\vDash \phi$ is true, then $T\vdash \phi$ 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 $\vDash F$ [or even if $\aleph _{0}$-$\vDash F$], then $\vdash F$. If $E_{1},...,E_{k}\vDash F$ [or even if $E_{1},...,E_{k}\ \aleph _{0}$-$\vDash F$], then $E_{1},...,E_{k}\vdash F$.
     (b) […]

Synonyms

• (state of being complete): completion, fulfillment; see also Thesaurus:completion

Antonyms

• incompleteness, unfinishedness; see also Thesaurus:incompletion

Derived terms

• completeness axiom

Translations

state or condition of being complete

• Bulgarian: ця́лостност (bg) (cjálostnost), завърше́ност (bg) (zavǎršénost)
• Chinese:

  Mandarin: 完整性 (zh) (wánzhěngxìng)

• Czech: úplnost f
• Esperanto: tuteco
• Finnish: täydellisyys (fi), valmius (fi)
• French: complétude (fr) f
• German: Vollständigkeit (de) f
• Greek:

  Ancient: ἐντέλεια f (entéleia)

• Hebrew: שלמות f (shlemut)
• Indonesian: kelengkapan (id)
• Irish: foirfeacht f
• Italian: completezza (it) f
• Polish: całkowitość f, kompletność (pl) f, zupełność (pl) f, pełnia (pl) f
• Portuguese: completidão f, completude (pt) f
• Russian: полнота́ (ru) f (polnotá), завершёность f (zaveršónostʹ), зако́нченнность f (zakónčennnostʹ), це́лостность (ru) f (célostnostʹ)
• Spanish: completitud (es) f
• Swedish: fullständighet (sv) c
• Turkish: bütünlük (tr)