Category talk:Zermelo-Fraenkel Axioms

I would prefer this page to be an entire article, and not a list of articles. Or we could at least explain all of the axioms in one article and link each axiom to a page that discusses the specific axiom in depth.

--Kal 02:19, 19 August 2008 (UTC)

What, like I did with the axioms of PropLog?

Yeah, needs to be done, I didn't do it myself for fear of making myself look even more stupid than I already am. Feel free to do this for me. ;-) --Matt Westwood 05:25, 19 August 2008 (UTC)

This may be a stupid question, but Wikipedia and Wolfram both only list 9 including AoC, Wolfram doesn't include the Axiom of Existance, saying it can be derived from the Axiom of Infinity and the Axiom of Subsets. Wikipedia uses different names for the Axioms, but presumably ignores the same one. What's up with that? --cynic 01:12, 15 September 2008 (UTC)

Actually I just looked, and there already is a page on this (the "entire article" that Kal was talking about?)

As for the Axiom of Existence, I quote what I originally wrote:

"The Axiom of Existence: There exists a set that has no elements.

This can be deduced from the Axiom of Infinity and Axiom of Subsets and some treatments exclude it from the list.

It is sometimes referred to as the Axiom of the Empty Set."

Wolfram has changed recently I'm he certainly *did* include Existence at one point. --Matt Westwood 05:21, 15 September 2008 (UTC)

Good call, as recently as April 2005 Wolfram listed "the Axiom of the Empty Set" under ZF Axioms (see [1]). --cynic 20:09, 15 September 2008 (UTC)