Talk:Axiom of Foundation (Strong Form)

What's the relationship between this and Axiom:Axiom of Foundation (Classes)?

They both seem to assert the existence of a minimal element (sorry, possibly obvious, I haven't kept up with all this class-theoretic stuff you've all been adding).

For that matter, is Axiom:Axiom of Foundation the same statement for sets?

And lastly, does it bother anyone else to have a proof of something labeled an Axiom (that is in the main/proof namespace)? --Alec (talk) 00:53, 26 August 2012 (UTC)


 * We're proving this within ZF set theory. We can't assume Axiom:Axiom of Foundation (Classes), which is not part of ZFC (it's part of NBG).  We can only assume Axiom:Axiom of Foundation, which is the analogous statement for sets.  The proof of the statement for classes is not obvious. --Andrew Salmon (talk) 01:09, 26 August 2012 (UTC)


 * I have added the category "Zermelo-Fraenkel Class Theory" to show that this is ZF specific. --Andrew Salmon (talk) 01:16, 26 August 2012 (UTC)


 * So we're going with the strategy that the two branches of set theory are completely divorced from one another? Fair enough, as long as I know what's been decided. --prime mover (talk) 09:02, 26 August 2012 (UTC)