Timeline for Definitional complexity of truth in $L$ without $0^{\#}$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 9, 2017 at 14:44 | vote | accept | Elliot Glazer | ||
| May 9, 2017 at 4:33 | comment | added | Elliot Glazer | Alright duly noted. | |
| May 9, 2017 at 4:32 | comment | added | Asaf Karagila♦ | For future reference, you can flag the question on MSE and ask for it to be migrated, instead of cross posting. It's cleaner that way... | |
| May 9, 2017 at 0:15 | answer | added | Joel David Hamkins | timeline score: 10 | |
| May 8, 2017 at 18:40 | comment | added | Elliot Glazer | You're right, the reason he made the definition this way was to create a predicate for truth with parameters in $L.$ So I guess the question is, for truth without parameters, can we make it $\Delta_n^1$ for some $n?$ | |
| May 8, 2017 at 18:01 | comment | added | Trevor Wilson | I think we can decrease the complexity a bit as follows. Given a regular cardinal $\kappa$ such that $L_\kappa \prec L$, we may force with the Levy collapse to make $\kappa = \omega_1$. Then $L_{\omega_1} \prec L$, and the first-order theory of $L_{\omega_1}$ is $\Sigma_\omega(H_{\omega_1},\in)$ and therefore $\Sigma^1_\omega$. | |
| May 8, 2017 at 16:02 | review | First posts | |||
| May 8, 2017 at 16:17 | |||||
| May 8, 2017 at 16:00 | history | asked | Elliot Glazer | CC BY-SA 3.0 |