Axiom talk:Axiom of Unions

Rename suggestion
It's called "Axiom of Unions" in Halmos, and IMO it's probably better to adhere to the printed works in preference to web resources as the latter are by their nature far less permanent. So IMO no rename. --prime mover (talk) 23:08, 28 December 2012 (UTC)


 * I see that Kelley uses different terminology altogether (General Topology, 1955) in the appendix that apparently was the first publication of Morse-Kelley set theory:
 * Page 258 Axiom of union: If $x$ is a set and $y$ is a set so is $x\cup y$.
 * Page 261 Axiom of amalgamation: If $x$ is a set so is $\bigcup x$. --Dfeuer (talk) 23:29, 28 December 2012 (UTC)


 * Once we have a hard citation for the singular, we can move to it, because it does appear to be more common than the plural. We wait till that time. --prime mover (talk) 23:35, 28 December 2012 (UTC)


 * In the mean time, I just created Axiom:Axiom of Union and Axiom:Axiom of Union/Morse-Kelley to reflect the source I have on hand. I could use some help in clarifying what goes with what and all. --Dfeuer (talk) 23:56, 28 December 2012 (UTC)

I'll bend a brain cell to it later. It's late and I need sleep. --prime mover (talk) 00:25, 29 December 2012 (UTC)

Refactoring according to Smullyan and Fitting
It's inelegant to refer to an axiom by means of the schema it is part of. It is far preferable to make the axioms independent of the schemata, and then include whichever into whatever according to the nature of the schema.

To that end I have differentiated the "Axiom of Union" (as used in Morse-Kelley) and the "Axiom of Unions" (as used in Zermelo-Fraenkel and NBG, and called the Axiom of Amalgamation in Morse-Kelley), according to the naming convention of Halmos.

It may be unconventional, but it gets us where we want to go. It will need to be weasel-worded in the Also known as and Also defined as sections of the various entities in question. This is work in progress. --prime mover (talk) 06:15, 26 January 2020 (EST)


 * Thus Axiom:Axiom of Union/Morse-Kelley is now Axiom:Axiom of Union, and Axiom:Axiom of Union/Zermelo-Fraenkel is now Axiom:Axiom of Unions. Axiom:Axiom of Amalgamation is now a redirect to Axiom:Axiom of Unions. --prime mover (talk) 07:02, 26 January 2020 (EST)