Timeline for Is every elementary absolute geometry Euclidean or hyperbolic?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 19, 2014 at 19:15 | vote | accept | Conifold | ||
| Sep 18, 2014 at 1:26 | comment | added | Conifold | Originally I was wondering if there are $H$-planes where any two segments have a common measure, so that excluded non-Archimedean ones. With the line-circle axiom the answer is negative also, as follows from Will Jagy's answer, but $HE$ seems trickier. | |
| Sep 18, 2014 at 1:25 | comment | added | Conifold | @Marvin Greenberg Thank you for the answer. Sorry, I confused formally real fields with real closed fields, one still has to take closure after adjoining square roots. I was hoping to avoid checking the axioms for the completion because according to Pambuccian's paper (p.19 public.asu.edu/~pusunac/papers/budapest21.pdf) the congruence of segments in $H$-planes is defined by a formula that dictates the metric to be a restriction of the usual Euclidean or hyperbolic. So after completion we should directly get $\mathbb{R}^2$ or a Klein disk with a standard metric? | |
| Sep 17, 2014 at 22:08 | comment | added | Will Jagy | Got your email. Hope the OP (Original Post-er) notices this, (s)he will be notified. | |
| Sep 17, 2014 at 21:34 | review | First posts | |||
| Sep 17, 2014 at 22:36 | |||||
| Sep 17, 2014 at 21:31 | history | answered | Marvin Greenberg | CC BY-SA 3.0 |