Timeline for History of well founded relations
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Oct 16 at 9:33 | history | edited | Paul Taylor | CC BY-SA 4.0 |
added translation of Mirimanoff
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| Sep 6, 2023 at 15:32 | comment | added | Joel David Hamkins | @PseudoNeo I saw what you did there. | |
| Sep 6, 2023 at 15:09 | comment | added | Paul Taylor | As the Postcript says, there is a historical introduction in my paper "Well founded coalgebras and recursion" that is perhaps already too long. The purpose of this Question was to fill in one specific gap in that history. Of course it would be nice to have a comprehensive history of induction, but I am not a qualified historian. Writing an up-to-date such history backwards would, I think, be even more difficult than writing it forwards! | |
| Sep 6, 2023 at 14:56 | comment | added | PseudoNeo | It would be better to tell the story backwards. You would be sure to finish at some point. | |
| Sep 6, 2023 at 14:29 | comment | added | Joel David Hamkins | I was thinking it gives a somewhat fuller historical picture, since not everything on your list is about that abstract well-founded concept. In particular, Dedekind's 1888 categoricity result for arithmetic (basically, any two inductive successor operations are isomorphic) amounts to a precursor and special case of the comparability result you mention of Cantor. And Cantor's earlier use of transfinite recursion in the Cantor-Bendixson theorem is the first nontrivial use of transfinite recursion, which I think of as absolutely central and indeed seminal in the history of well-foundedness. | |
| Sep 6, 2023 at 14:25 | comment | added | Paul Taylor | @JoelDavidHamkins. Yes of course. But I was looking specifically for the abstract notion well founded relation, as classically stated. There's another question about who first stated it intuitionisticallly, ie just as the induction scheme. However, that is much more difficult because of the habit of intuitionists to state classical definitions and then argue at length about why they're wrong, instead of just giving the correct constructive definition. | |
| Sep 6, 2023 at 14:18 | comment | added | Joel David Hamkins | What about Dedekind arithmetic (1888), which states induction for the natural numbers with successor, and Peano's (1889) subsequent beautiful and popular use of it to develop the basics of number theory. Also, Cantor made essential use of transfinite recursion in the Cantor-Bendixson theorem (1872), and indeed, these ideas are what led him to the ordinals. | |
| Sep 6, 2023 at 14:09 | history | edited | Paul Taylor | CC BY-SA 4.0 |
added 712 characters in body
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| May 24, 2020 at 23:57 | answer | added | George S Cowan | timeline score: 2 | |
| Apr 15, 2020 at 11:03 | history | edited | Paul Taylor | CC BY-SA 4.0 |
added set theory tag; minor typo
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| Apr 14, 2020 at 19:05 | history | edited | Andrej Bauer | CC BY-SA 4.0 |
spelling
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| Apr 14, 2020 at 14:32 | history | edited | Paul Taylor | CC BY-SA 4.0 |
changed title
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| Apr 12, 2020 at 11:40 | history | asked | Paul Taylor | CC BY-SA 4.0 |