Timeline for How can a subset of reals not exist?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 21 at 16:25 | vote | accept | Maxim | ||
| Apr 19 at 23:24 | history | removed from network questions | Asaf Karagila♦ | ||
| Apr 19 at 23:14 | history | became hot network question | |||
| Apr 19 at 19:50 | answer | added | Asaf Karagila♦ | timeline score: 2 | |
| Apr 19 at 17:11 | comment | added | Dave L. Renfro | I don't know these things in detail, but I do know that one needs to be VERY careful in dealing with non-ZFC models of set theory, since quite often standard results one has learned and standard methods one has used for many years might not hold in the model. | |
| Apr 19 at 17:10 | answer | added | Andreas Blass | timeline score: 12 | |
| Apr 19 at 16:46 | comment | added | Maxim | @DaveL.Renfro But the proof of non-measurability of a Vitali set doesn't seem to rely on the Axiom of Choice. And the construction of real numbers doesn't rely on AC. So can't we construct two identical sets of real numbers in both models, then only invoke AC to find a Vitali set in the ZFC model, then map the elements, and finally for the mapped set prove non-measurability inside the Solovay model? | |
| Apr 19 at 16:07 | comment | added | Dave L. Renfro | I think the problem is that in the Solovay model you are unable to prove that the mapped set is not measurable (in fact, in the Solovay model the set WILL BE measurable). As an analogy, the (geometric) $2$-sphere as a model for a certain non-Euclidean geometry is such that there is a certain (provable) theorem involving parallel lines, but if you map this $2$-sphere to the model of ordinary Euclidean $3$-space, then the theorem can no longer be proved (in fact, in the Euclidean model the statement WILL BE false). | |
| Apr 19 at 15:15 | comment | added | Glinka | My guess would be that the problem is somehow with the mapping... | |
| Apr 19 at 15:08 | history | asked | Maxim | CC BY-SA 4.0 |