Timeline for A principle of mathematical induction for partially ordered sets with infima?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 19, 2019 at 4:49 | history | edited | François G. Dorais | CC BY-SA 4.0 |
typo
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| Sep 11, 2010 at 20:24 | comment | added | Joel David Hamkins | András, yes, in that terminology, I am talking here just about complete lattices, which I had viewed as the natural context for the question. But perhaps one can find an induction-like characterization of CPOs? Give it a shot! Pete, thanks for accepting! But of course, it was also fine when you had accepted François' answer... | |
| Sep 11, 2010 at 19:07 | comment | added | Pete L. Clark | Excellent! Thanks to both Joel and François -- as ever, I can only accept one answer. I think this is a real MO success story. | |
| Sep 11, 2010 at 19:04 | vote | accept | Pete L. Clark | ||
| Sep 11, 2010 at 18:30 | comment | added | András Salamon | The "lt" in part 2 seems to be missing the backslash. | |
| Sep 11, 2010 at 18:29 | comment | added | András Salamon | Notational nit: in the terminology I am familiar with, a complete partial order (cpo) is a strictly more general notion than a complete lattice. en.wikipedia.org/wiki/Complete_partial_order | |
| Sep 10, 2010 at 20:14 | comment | added | Joel David Hamkins | I also wonder this---I played around with many variations before hitting on this one. Your argument avoiding (1) in effect uses completeness, and I don't know any nice characterization avoiding (1) without assuming some completeness. Another question is: can we get a nice characterization that doesn't require the maximal element? I need this in order to know $sup(S)$ exists, and don't have any nice characterization without the maximal element. | |
| Sep 10, 2010 at 18:25 | comment | added | François G. Dorais | Nice answer, Joel! I still wonder, since my condition 1 was not necessary, whether there is a variation of just 2 & 3 that has an if-and-only-if characterization. | |
| Sep 10, 2010 at 17:50 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
added 143 characters in body
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| Sep 10, 2010 at 11:41 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
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| Sep 10, 2010 at 11:20 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |