# completeness

## English

Wikipedia has an article on:

Wikipedia

### 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 $T \vDash \phi$ is true, then $T \vdash \phi$ must also be true, for any wff φ of logic L.