Timeline for Higman's lemma and a manuscript of Erdős and Rado
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Oct 30, 2019 at 6:36 | comment | added | user6976 | @bof: Sorry, here is a question on mathSE and a comment by Robert Israel there which contains a complete proof (three lines). I do not claim that it originates with Dilworth. I simply always call it, probably incorrectly, "an infinite version of Dilworth theorem". | |
| Oct 29, 2019 at 21:00 | comment | added | bof | @MarkSapir You refer me to a Wiki page on Dilworth's decomposition theorem? I've known about Dilworth's theorem for many years. Of course the fact that "every infinite poset contains an infinite chain or antichain" can be seen as a corollary of Dilworth's theorem, just as it is a corollary of Ramsey's theorem. However, I would have thought the simple observation that "every infinite poset contains an infinite chain or antichain" was known long before the contributions of Dilworth (1950) or Ramsey (1930), and I wanted to know if you had a source for claiming that it originated with Dilworth. | |
| Oct 29, 2019 at 17:32 | comment | added | user6976 | @bof: See en.wikipedia.org/wiki/… | |
| Aug 27, 2019 at 2:01 | comment | added | bof | @MarkSapir Do you have a reference for the attribution to Dilworth of the observation that every infinite poset contains an infinite chain or an infinite antichain? | |
| Aug 26, 2019 at 15:13 | vote | accept | Salvo Tringali | ||
| Aug 26, 2019 at 9:48 | comment | added | user6976 | The formulation of Dilworth theorem is in my previous comment. | |
| Aug 26, 2019 at 6:51 | comment | added | Salvo Tringali | @MarkSapir I join bof in their request. I guess you refer to the extension of Dilworth's thm to infinite posets (en.wikipedia.org/wiki/…), don't you? | |
| Aug 26, 2019 at 1:59 | comment | added | user6976 | It follows immediately from Dilworth theorem: every infinite poset contains either an infinite chain or an infinite antichain. This is an easy (high school level) statement. | |
| Aug 26, 2019 at 1:07 | history | became hot network question | |||
| Aug 25, 2019 at 22:15 | history | edited | Salvo Tringali | CC BY-SA 4.0 |
fixed a mistake pointed out by Andreas Blass in the 1st version of his answer
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| Aug 25, 2019 at 22:00 | comment | added | Andreas Blass | Yes, I mean the infinite Ramsey theorem. I've put the proof into an answer, since it's too long for a comment. | |
| Aug 25, 2019 at 21:59 | answer | added | Andreas Blass | timeline score: 8 | |
| Aug 25, 2019 at 20:56 | history | edited | Salvo Tringali | CC BY-SA 4.0 |
fixed a reference and added some details about the proof of Theorem
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| Aug 25, 2019 at 20:17 | comment | added | Salvo Tringali | @AndreasBlass Do you mean the infinite Ramsey thm (en.wikipedia.org/wiki/Ramsey's_theorem)? If so, could you explain in some detail how to use it to prove the equivalence between (a) and (b), if this is what you mean by "this thm of Higman"? | |
| Aug 25, 2019 at 19:34 | comment | added | Andreas Blass | Unless I've misunderstood something, this theorem of Higman is an immediate consequence of Ramsey's theorem (which might have been rediscovered by Erdös and Rado). | |
| Aug 25, 2019 at 17:04 | answer | added | Vince Vatter | timeline score: 11 | |
| Aug 25, 2019 at 16:52 | history | edited | Salvo Tringali | CC BY-SA 4.0 |
deleted 43 characters in body
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| Aug 25, 2019 at 16:38 | history | asked | Salvo Tringali | CC BY-SA 4.0 |