Timeline for Is there any standard name for Provably Decidable Set?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 7, 2016 at 11:46 | comment | added | Payam Seraji | You are wellcome. | |
| Aug 7, 2016 at 7:55 | comment | added | Erfan Khaniki | @PayamSeraji: Interesting comment. Thank you. | |
| Aug 6, 2016 at 20:00 | comment | added | Payam Seraji | For all levels of the arithmetical hierarchy ($\Sigma_n$, $\Pi_n$, $\Delta_n$), a definable set $A$ my be (for example) "$\Sigma_n$ in the standard model of arithetic" or "provabily $\Sigma_n$ in $T$). Obviously the later implies the former (if $T$ is sound) but the converse is not necessarily true. So I think another name for your concept is "provabily (in $T$) $\Delta_1$". | |
| Aug 6, 2016 at 0:46 | comment | added | Erfan Khaniki | @NoahSchweber:I mean $T$ is in language of arithmetic($\mathcal{L}_T=\{0,S,+,\cdot\}$) | |
| Aug 6, 2016 at 0:26 | comment | added | Noah Schweber | What does "arithmetical" mean here? (Since $T$ is recursively enumerable, it's certainly arithmetical in the computability-theoretic sense . . .) | |
| Aug 5, 2016 at 18:12 | history | edited | Erfan Khaniki | CC BY-SA 3.0 |
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| Aug 5, 2016 at 18:11 | comment | added | Erfan Khaniki | @JoelDavidHamkins: I edited my post. about your third question, Is there any difference for definition of provably decidable set if for example $I\Delta_0\subseteq T$ ? | |
| Aug 5, 2016 at 18:05 | history | edited | Erfan Khaniki | CC BY-SA 3.0 |
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| Aug 5, 2016 at 17:31 | comment | added | Joel David Hamkins | Could you clarify whether you intend to assume that $T$ is computably enumerable? Or that $T$ is true in the standard model? Or that $T$ contains some specific weak theory? | |
| Aug 5, 2016 at 17:13 | history | asked | Erfan Khaniki | CC BY-SA 3.0 |