Definition:Theory (Logic)/Complete

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Definition

Let $\mathcal L$ be a language.

Let $T$ be an $\mathcal L$-theory.


$T$ is complete if and only if:

for every $\mathcal L$-sentence $\phi$, either $T \models \phi$ or $T \models \neg \phi$

where $T \models \phi$ denotes semantic entailment.