On Wed, Jun 29, 2011 at 4:43 AM, James Lipton <jlipton@wesleyan.edu> wrote:
These are the "hereditarily finite sets"
V(0) = empty set
V(n+1) = P(V(n))
V(omega) = U{V(n): n in omega}
I would not call it "the" cat of finite sets, since there uncountably many countable models of ZF. Obviously the choice of ZF, rather than say Zermelo set theory or some other foundation is also pretty arbitrary.
I should think that the hereditarily finite sets do not depend all that much on the background setting. After all, there are not very many of them and they are quite concrete. Can they really be hugely different depending on whether we work in ZF, ZFC, IZF, CZF etc? With kind regards, Andrej [For admin and other information see: http://www.mta.ca/~cat-dist/ ]