Axiom talk:Axiom of Empty Set

I believe that this page should be renamed to "Axiom of the Empty Set", because there is already an axiom for set theory that asserts the existence of some set, and I think that "Axiom of Existence" would be a more fitting title for it.

Also, according to this page, this axiom could be deduced by the axiom of subsets alone. I'm just throwing it out there. --HumblePi (talk) 13:53, 16 April 2017 (EDT)


 * It's what it's generally called though, so that's what its name is here. --prime mover (talk) 14:00, 16 April 2017 (EDT)


 * Ok, so what should the axiom that I mentioned be called then? --HumblePi (talk) 14:16, 16 April 2017 (EDT)


 * My understanding is that the axiom of existence is the axiom that states that there exists a set, and it is the empty set. I also understand that there are a number of axioms that one can take as "the" axioms of set theory, as the usual ZFC ones are to a certain extent interderivable, and I also point out that there are many different axiom schemas which can be used, and that this one was picked because it was the one in the particular books I had access to. --prime mover (talk) 15:49, 16 April 2017 (EDT)

Thinking further, your plan has merit. Ultimately we want to document all the axiom schemas which have been used in the literature to axiomatise set theory, so I suppose it makes sense to call them by a unique and unambiguous name. --prime mover (talk) 17:16, 16 April 2017 (EDT)


 * As suggested. --prime mover (talk) 11:59, 17 April 2017 (EDT)