Timeline for Which ordinals can be embedded into an ordered field?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 11, 2016 at 0:01 | vote | accept | Haidar | ||
| Mar 10, 2016 at 18:18 | comment | added | Emil Jeřábek | @nombre It can’t be, because of the Erdős–Rado theorem; this is mentioned in my answer. | |
| Mar 10, 2016 at 18:12 | answer | added | Emil Jeřábek | timeline score: 8 | |
| Mar 6, 2016 at 13:32 | comment | added | nombre | As Joel David Hamkins said, this ordinal is not bounded by any function of cofinality. One can also prove that this ordinal is regular so it is a cardinal. I wonder if it can be that $2^{\alpha} < |F|$? | |
| Mar 4, 2016 at 18:10 | comment | added | Joel David Hamkins | The issue of "bounded" seems moot, since if an ordinal $\beta$ embeds into a field at all, then it embeds into a bounded interval, by first translating to the positives and then composing with $x\mapsto -\frac 1x$. | |
| Mar 4, 2016 at 16:59 | answer | added | Joel David Hamkins | timeline score: 8 | |
| Mar 4, 2016 at 16:15 | comment | added | Haidar | I wonder if the answer, in general, can be specified in terms of certain properties of the ordered field, like its cofinality. | |
| Mar 4, 2016 at 16:11 | comment | added | Emil Jeřábek | This depends entirely on the field. What kind of an answer are you looking for? | |
| Mar 4, 2016 at 16:00 | history | asked | Haidar | CC BY-SA 3.0 |