TITLE: Advantages of finite axiomatizability
QUESTION [9 upvotes]: I've seen it written in a number of places that one of the "advantages" of NBG over ZFC is that it is finitely axiomatizable.
I was wondering, what are some examples of how this is advantageous?
I see no philosophical advantage of finite, as opposed to recursively enumerable, axiomitization since it's always seemed the important thing is being to effectively decide whether or not a statement is an axiom. Plus, there are usually an infinite number of logical axioms around anyway, though I suppose this isn't essential.
So I guess I'm interested in practical advantages. On the other hand, I haven't thought very deeply about possible philosophical advantages, so if I'm missing something there, feel free to discuss that as well.

REPLY [2 votes]: Philosophically, one could argue that having a finite set of axioms is a more concrete situation than having an infinite but decidable set of axioms. Depending on taste, having a finite set of axioms may be seen as more elegant, or as conceptually simpler.  It may help to think of the fact that a finite set of axioms can be replaced with just one axiom, the conjunction of the finite set. So the real difference is between having just one axiom, or infinitely many.