completeness

noun
  1. 1

    The state or condition of being complete

  2. 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 \vDash \phi is true, then T \vdash \phi must also be true, for any wff ฯ† of logic L.

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Source: https://en.wiktionary.org/wiki/completeness

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