Timeline for Sets that are not $\infty$-Borel
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Mar 4, 2016 at 20:14 | comment | added | Paul Larson | I believe that Trevor and I have worked out an answer to (1). Add infinitely many Cohen reals over $L$, with finite support. Now consider $L(A, S)$, where $A$ is the set of reals $E_0$-equivalent to one of the generic reals, and $S$ is the $\omega$-sequence of $E_0$-degrees. If you want to have DC as well, add $\omega_1$ many Cohen reals instead, and take $L(R, S)$, where $R$ is the set of all reals from the forcing extension, and $S$ is as before, with the corresponding sequence. Rumour has it that Woodin has constructed a similar example. | |
| Jul 14, 2014 at 13:09 | comment | added | Paul Larson | The forcing also adds no functions from the ordinals to the ground model. So the extension won't be a counterexample to (1), unless the ground model is. | |
| Jul 6, 2014 at 20:21 | vote | accept | Trevor Wilson | ||
| Jul 6, 2014 at 8:00 | history | answered | Paul Larson | CC BY-SA 3.0 |