 We note that we do not need an axiom asserting the existence of \(\varnothing\) (which is frequently included in axiom lists as it was in Zermelo’s original axiom set): the existence of any object (guaranteed by logic unless we use a free logic) along with separation will do the trick, and even if we use a free logic the set provided by Infinity will serve (the axiom of Infinity can be reframed to say that there is a set which contains all sets with no elements (without presupposing that there are any) and is closed under the desired successor operation).