Timeline for A principle of mathematical induction for partially ordered sets with infima?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 19, 2019 at 11:57 | comment | added | ABIM | Alright, I just may do that :) Merci Francois. | |
| Feb 19, 2019 at 4:43 | comment | added | François G. Dorais | @AIM_BLB As the post explains, I came up with this theorem after reading Pete L. Clark 's post somewhere between September 9 and September 10, 2010. I couldn't possibly claim originality here: it's very likely someone else came up with this before me but I have no idea if anyone published this before. (If you're looking for a citation, the 'cite' button will give you what you need.) | |
| Feb 18, 2019 at 13:30 | comment | added | ABIM | Do you have a reference for this wonderful theorem? | |
| Sep 10, 2010 at 2:03 | comment | added | Pete L. Clark | I agree -- I'm looking for an iff as well. Let me know if you come up with anything. | |
| Sep 10, 2010 at 1:49 | comment | added | François G. Dorais | @Joel: Yes, I've been thinking about Pete's if-and-only-if characterization of completeness too but I haven't found any good leads. | |
| Sep 10, 2010 at 1:42 | comment | added | Joel David Hamkins | François, I've been looking at the same idea! But this gives only one direction of Pete's iff. For example, a partial order consisting of a single antichain has your inductive property vacuously, since there are no inductive sets, but it does not have greatest lower bounds for all subsets (for example, there is no minimal element). I think we should be able to find an if-and-only-if characterization! | |
| Sep 10, 2010 at 1:37 | vote | accept | Pete L. Clark | ||
| Sep 11, 2010 at 19:04 | |||||
| Sep 10, 2010 at 1:33 | history | edited | François G. Dorais | CC BY-SA 2.5 |
addendum
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| Sep 10, 2010 at 1:18 | comment | added | Pete L. Clark | @Francois: I will need to check this over, but if it works as you say (of which I have very little real doubt), then this will absolutely be the answer to my question! Note that the distinction between $S$ and $S'$ is analogous to the distinction between "weak" versus "strong" induction, and it's something I had been thinking about as well. | |
| Sep 10, 2010 at 1:01 | history | answered | François G. Dorais | CC BY-SA 2.5 |