Timeline for Is non-existence of the hyperreals consistent with ZF?

10 events

when toggle format	what		by	license	comment
Apr 13, 2017 at 12:57	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Dec 23, 2014 at 3:11	vote	accept	Arseniy Sheydvasser
Dec 8, 2014 at 23:46	comment	added	Ali Enayat		A small remark: in ZF the existence of a proper elementary extension of the structure $(\Bbb{N}, X)_{X\in\cal{P}(\omega)}$ is equivalent to the existence of a nonprincipal ultrafilter on $\Bbb{N}$. Joel has explained one direction, the other direction uses a standard ultrapower argument (the Łoś-theorem goes through in the absence of choice in this case since $\Bbb{N}$ is well-orderable).
Dec 4, 2014 at 14:14	history	edited	Joel David Hamkins	CC BY-SA 3.0	Forgot the empty set!
Dec 4, 2014 at 13:11	history	edited	Joel David Hamkins	CC BY-SA 3.0	fixed various issues
Dec 4, 2014 at 12:29	history	edited	Joel David Hamkins	CC BY-SA 3.0	added 482 characters in body
Dec 4, 2014 at 10:42	comment	added	Asaf Karagila♦		It might be worth pointing that it is consistent with $\sf ZF$ that there are no free ultrafilters on $\Bbb N$. And for that matter, on any set.
Dec 4, 2014 at 2:30	history	edited	Joel David Hamkins	CC BY-SA 3.0	added 2 characters in body
Dec 4, 2014 at 2:23	history	edited	Joel David Hamkins	CC BY-SA 3.0	added 2 characters in body
Dec 4, 2014 at 2:17	history	answered	Joel David Hamkins	CC BY-SA 3.0