Timeline for Additive Subgroups of the Reals.
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
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| Mar 29, 2011 at 22:15 | vote | accept | Alex | ||
| Mar 29, 2011 at 22:16 | |||||
| Mar 29, 2011 at 17:20 | comment | added | James Freitag | And although this is in another direction of hopeless complication, adding a finite rank additive subgroup to the reals with the field structure allows one to define the integers. To see this, take the set of reals for which multiplication by $r$ is a map from $G \rightarrow G.$ Take the fraction field of this set. This is a finite degree extension of $\mathbb{Q}.$ Now results of J. Robinson give the definability of the integers. So, this is another instance of hopeless complication. | |
| Mar 29, 2011 at 16:49 | history | answered | Juris Steprans | CC BY-SA 2.5 |