1. Describes any deductive system for which there exists a finite set of formulae from which all formulae may be derived, i.e., for which the deductive closure of is the language itself. Some paraconsistent logics, for example, are not finitely trivializable (although others—like C-systems—are finitely trivializable).
2. Describes a theory with respect to a deductive system when there exists a finite set of sentences such that the deductive closure of under is the entire language.