consistent

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

A slightly different definition is sometimes used, that $T$ is consistent iff $T\not\vdash\bot$ (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.