 by using ‘\(\rE!\)’ to restrict specification. (A4) stipulates in effect that the quantifiers range over all objects that satisfy ‘\(\rE!\)’, (A5) that they range only over objects that satisfy ‘E!’. Omitting (A5) and replacing (A4) with (A4c) yields classical logic. To obtain a non-inclusive free logic, we may add to (A1)–(A5) the axiom \(\exists x\rE!x\)—or any axiom of the form \(\exists xT\) such that for any term \(t, T(t/x)\) is a tautology.