Axiom talk:Axiom of Limitation of Size

At the point that this axiom is raised, are we sure that there is actually a "universe" defined? One of the interesting things about ZFC is that there is no such concept as a "universe" and at this stage it can only be an intuitive concept at best, as it can not be inferred from ZFC itself.

In the context of the Godel-Bernays Axioms, it may well be that the universe is defined (I haven't investigated in detail, it's on my bucket list) - and if so it needs to be specifically referenced in that page. We also need to check that it goes to the appropriate page - at the moment "Universe" is a disambiguation page. I suspect we may need either to add a new page to explain what it is in Class Theory or extend the "Universe (Set Theory)" page to suit. --prime mover 06:35, 19 June 2011 (CDT)

In reply to the explain tag, and also to the above, old, remark, note that on the main Godel-Bernays page, under "Axioms for Sets" the "universe" is also mentioned. — Lord_Farin (talk) 13:54, 21 January 2020 (EST)

I'm gradually getting to grips with NBG (which may or may not coincide completely with Godel-Bernays or it maybe a subtle variant of it) and my understanding of a "universal class" has expanded. Smullyan and Fitting are very accessible and intelligently presented, and under its influence I'm completely redesigning the way we present this sort of material.

Feel free to comment on anything concerning the direction I'm trying to point this thing in; you never know, I may even see if I can get a copy of the Takeushi and Zaring to reconcile the pioneering work done by Asalmon. Now we have access to the complete thread of thought in class theory I can piece together some of the gaps in that presentation that made it more than a bit puzzling. Turns out it's more coherent than I thought. --prime mover (talk) 15:23, 21 January 2020 (EST)