This analogy is a conceptual one, and is only tenuously related to the size of the carrier sets. The algebraic definitions are also distinguishable even in classical logic. It has no finite presentation. However, there is no other implication. We shall compare and contrast these definitions further in Proposition 6.6.13 ff.
G is epi.
Now consider the introduction and elimination rules for the quantifier. The premise of the introduction rule is just a listing. In the elimination rule, q must not depend in any way on the listing, ie n , i , or x i . But this box, like all others, must be properly nested. However, there are problems with counting even when we seem to be able to identify a specific number of distinct things.