 Maximal consistent set of first-order sentences

A consistent set of first-order sentences is maximal when adding any new sentence makes it inconsistent. It is then deductively closed and decides every sentence by containing exactly one of it and its negation. Conversely a consistent deductively closed set that decides every sentence is maximal. Merely listing a finite axiom set for a complete theory does not make that raw list maximal: maximality applies to the deductive closure.