From owner-cse191-sp08-list@LISTSERV.BUFFALO.EDU Sat Mar 1 16:59:40 2008 Date: Sat, 1 Mar 2008 16:58:31 -0500 From: "William J. Rapaport" Subject: 191: Axioms for Set Theory To: CSE191-SP08-LIST@LISTSERV.BUFFALO.EDU ------------------------------------------------------------------------ Subject: 191: Axioms for Set Theory ------------------------------------------------------------------------ When we began discussing sets, I mentioned that one approach to set theory is to take the notions of set, member, and the set-membership relation as primitive (i.e., undefined), and then provide axioms for them. There are two major sets of axioms: Zermelo-Fraenkel axioms (ZF) and von Neumann-Bernays-Goedel axioms (NBG). Most mathematicians prefer the ZF axioms, even though von Neumann and Goedel are more well known to computer scientists. (I remember when I was in graduate school, one of my logic professors described NBG set theory as standing for "No Bloody Good" :-) Anyway, the ZF axioms can be found at: http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html You might find that trying to read and understand them is a good way to practice your FOPL reading skills :-)