= Maximal consistent set of first-order sentences
= Maximal consistent
{synonym}
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.
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