Timeline for A question about formulating first order axioms for group theory.

8 events

when toggle format	what		by	license	comment
S Oct 21, 2012 at 18:42	vote	accept	Garabed Gulbenkian
S Oct 21, 2012 at 18:42	vote	accept	Garabed Gulbenkian
S Oct 21, 2012 at 18:42
Oct 21, 2012 at 18:41	vote	accept	Garabed Gulbenkian
S Oct 21, 2012 at 18:42
Oct 20, 2012 at 21:06	answer	added	Noah Schweber		timeline score: 3
Oct 20, 2012 at 20:59	answer	added	Andreas Blass		timeline score: 4
Oct 20, 2012 at 20:34	comment	added	Will Sawin		Presumably, what you are looking for is a relatively elegant axiom system in which the proof of the classification of finite simple sporadic groups is possible and that proof approximates the standard proof of the classification in ZFC. I have no idea if such a thing is possible.
Oct 20, 2012 at 20:31	comment	added	Will Sawin		The key problem seems to me that, naively, finite and simple are second-order properties, whereas sporadic naively might mean "not part of a nice infinite family of finite simple groups" or "not a cyclic group, an alternating group, or a Chevalley group" or something else that's hard to axiomatize elegantly. There are indeed many first-order axiom systems whose only models are the 26 finite simple sporadic groups, but by completeness they are all equivalent.
Oct 20, 2012 at 20:14	history	asked	Garabed Gulbenkian	CC BY-SA 3.0