Timeline for Fixed point theorems

Current License: CC BY-SA 4.0

8 events

when toggle format	what		by	license	comment
Dec 19, 2022 at 13:53	history	edited	Martin Sleziak	CC BY-SA 4.0	http -> https (the question was bumped anyway)
Dec 8, 2022 at 1:50	comment	added	Todd Trimble		That's great -- thank you very much, Paul.
Dec 8, 2022 at 0:50	comment	added	Paul Taylor		Todd Wilson, "An Intuitionistic Version of Zermelo's Proof that Every Choice Set can be Well-Ordered" JSL 66 (2001) 1121-6 doi 10.2307/2695096
Dec 7, 2022 at 23:23	comment	added	Todd Trimble		@PaulTaylor Well, Bauer and Lumsdaine are saying that Bourbaki-Witt is not constructive in the sense that it holds in all toposes, so I'm still confused by your remark. Could I trouble you for the title of Wilson's paper? I may ask Andrej or Peter to comment.
Dec 7, 2022 at 18:34	comment	added	Paul Taylor		I too was suspicious of (the other) Todd's paper when I first heard about it. What it actually shows is that the proof of B-W and in Zermelo's second proof as narrowly understood does not in fact use EM. However, the "well ordered" property that he derives is the classical one, ie every non-empty subset has a least element.
Dec 7, 2022 at 17:53	comment	added	Todd Trimble		@PaulTaylor Then I think I want to know what people mean by "constructive", because Bauer and Lumsdaine claim it cannot be proven intuitionistically (and I believe them), here: arxiv.org/abs/1201.0340. Can you shed some light on this?
Dec 7, 2022 at 17:12	comment	added	Paul Taylor		The Wikipedia page about Bourbaki-Witt gives the correct citations but wrongly states that the proof is by transfinite recursion. In fact, the argument is already in Zermelo's second (1908) proof of well-ordering. Todd Wilson has shown that the argument is constructive, apart from the fact that its result is the classical form of well-ordering.
Apr 10, 2013 at 20:07	history	answered	Todd Trimble	CC BY-SA 3.0