Timeline for Problem with definability in the constructible hierarchy
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 24, 2017 at 12:20 | vote | accept | Archimondain | ||
| Feb 22, 2017 at 18:07 | answer | added | Archimondain | timeline score: 3 | |
| Feb 22, 2017 at 11:27 | comment | added | Archimondain | The ordinal $\alpha$ is not the largest of $J_{\alpha+1}$: The ordinals of some class $J_{\beta+1}$ are all those strictly smaller than $\omega \beta + \omega$ (this is the Jensen hierarchy and not Godel's one). Also at the end I simply consider the exemple where $\alpha = \omega_1$. | |
| Feb 22, 2017 at 10:23 | comment | added | Mohammad Golshani | That $\alpha$ is simply definable in $J_{\alpha+1}$ does not follow from the simple fact that it is the largest ordinal in the structure? I don't understand how you transfer from $J_{\alpha+1}$ to $J_{\omega+1}$: You claim $\alpha$ is $\Sigma_2$-definable in $J_{\alpha+1}$, and then conclude the same in $J_{\omega_1+1}$, but how this is possible without referring to $\alpha$ itself? | |
| Feb 21, 2017 at 16:27 | history | asked | Archimondain | CC BY-SA 3.0 |