Timeline for The Importance of ZF
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 15, 2012 at 16:53 | comment | added | Joel David Hamkins | Regarding the parenthetical remark in the first sentence, the existence of universes is not a conservative extension of ZFC, since from the existence of a universe, one can prove new assertions, even new arithmetic assertions such as Con(ZFC), that we cannot prove in ZFC assuming it is consistent. | |
| Feb 10, 2010 at 6:05 | history | made wiki | Post Made Community Wiki by Harry Gindi | ||
| Nov 21, 2009 at 0:54 | comment | added | Tom Leinster | To expand on Qiaochu's comment: ETCS (Lawvere's Elementary Theory of the Category of Sets) is a counterexample to fpqc's feeling. That is, it's a useful alternative set theory that isn't equivalent to or stronger than ZFC. It's weaker, but still allows development of a very great deal of mathematics (say, all of a typical undergraduate programme). Compare Joel David Hamkins's answer, where he points out that "most" known theorems can be proved using only a relatively weak set theory. | |
| Nov 14, 2009 at 21:09 | comment | added | Qiaochu Yuan | In particular, see ncatlab.org/nlab/show/ETCS . | |
| Nov 14, 2009 at 20:48 | history | answered | Harry Gindi | CC BY-SA 2.5 |