Timeline for Hilbert style axioms for Euclidean and/or hyperbolic geometry without reference to congruence?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 2, 2012 at 20:44 | comment | added | David Feldman | So, if I understand, in terms of the coordinate ring, between-ness and Pappus will give us an ordered field. Then we also want it real-closed, so we can throw Dedekind completeness at it. But unfortunately, that assumption is second-order. I guess one doesn't expect finite first-order axioms for real-closed, but rather degree-by-degree axioms. Then these should translate into statements about configurations, perhaps in some clean and clever way? | |
| Sep 2, 2012 at 18:15 | comment | added | Will Jagy | @David, I thought about it overnight, and i am also not so sure that I know what you have in mind. I will leave the comment. I also agree with Robert that Marvin would know, but there is the problem of formulating the problem in terms he would like. I helped with a tiny part of the revisions for his fourth edition. Here is a page about his related article, a pdf can be downloaded from it: mathdl.maa.org/mathDL/22/… | |
| Sep 2, 2012 at 17:38 | comment | added | Robert Bryant | @John: Oh, yes. That's a very good point! Indeed, I should have gone for Pappus. | |
| Sep 2, 2012 at 15:59 | comment | added | John Stillwell | Maybe take Pappus instead Desargues, to ensure that the coordinates form a field instead of just a skew field. In any case, Pappus implies Desargues. | |
| Sep 2, 2012 at 14:22 | history | answered | Robert Bryant | CC BY-SA 3.0 |