Reading John Nolt's "Free Logic" article I see the symbol "E!" in the "2.1 Axiom Systems".
The following axioms are special for free logics.
(A4) ∀xA→(E!t→A(t/x)) (A5) ∀xE!x
(A4) modifies the classical principle:
by using ‘E!’ to restrict specification. (A4) stipulates in effect that the quantifiers range over all objects that satisfy ‘E!’, (A5) that they range only over objects that satisfy ‘E!’. Omitting (A5) and replacing (A4) with (A4c) yields classical logic.
Could someone explain what this specification restriction is? An alternate reference would also be helpful.
I am familiar with the uniqueness quantifier "∃!", but I don't think that is what is involved here.
Nolt, John, "Free Logic", The Stanford Encyclopedia of Philosophy (Fall 2018 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/fall2018/entries/logic-free/.