A <complete theory> is a consistent <first-order theory> deciding every sentence in its language:
$$
\boxed{T\models\sigma\quad\text{or}\quad T\models\neg\sigma\quad\text{for every }L\text{-sentence }\sigma.}
$$
Equivalently, every two <first-order models> of $T$ are <elementarily equivalent>. Consistency excludes the vacuous situation in which a <first-order theory> has no <first-order models> and entails both alternatives.

Solution

Past exam of the model theory course of the University of Oxford / 2011 / 2 / a / i / Solution

 Solution (source code)