consistent

If $T$ is a theory of $ℒ$ then it is consistent iff there is some model $ℳ$ of $ℒ$ such that $ℳ\models T$. If a theory is not consistent then it is inconsistent.

A slightly different definition is sometimes used, that $T$ is consistent iff $T⊬\perp$ (that is, as long as it does not prove a contradiction). As long as the proof calculus used is sound and complete, these two definitions are equivalent.