Timeline for The relation between $\Pi_1$-Foundation and $\Sigma_1$-Foundation over Kripke-Platek set theory
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 4, 2023 at 2:01 | comment | added | Hanul Jeon | @AliEnayat That is true that the subscript 0 looks attached to $\omega$ instead of the whole theory, I cannot deny that, so I swapped the order of 0 and $\omega$. | |
| Apr 4, 2023 at 1:59 | history | edited | Hanul Jeon | CC BY-SA 4.0 |
edited body
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| Apr 3, 2023 at 18:32 | comment | added | Ali Enayat | @HanulJeon Yes, there is no standard terminology here (for example in the older references $\mathsf{KP}$ includes the full scheme of foundation (equivalently, the full scheme of $\in$-induction). The problem I have with your current notation is that the subscript 0 visually seems to be attached to $\omega$, as opposed the whole package $\mathsf{KF}_{\omega}$, which is how you intend it. | |
| Apr 2, 2023 at 17:54 | comment | added | Hanul Jeon | @AliEnayat I did not use it because some references use KPI to denote KP with cofinality many recursively inaccessible ordinals. | |
| Apr 1, 2023 at 15:18 | comment | added | Ali Enayat | @HanulJeon Just a notational suggestion for long term purposes: $\mathsf{KPI}_0$ instead of $\mathsf{KP}_{\omega_0}$ , which is more in tune with other existing notation. | |
| Mar 27, 2023 at 3:56 | history | edited | Hanul Jeon | CC BY-SA 4.0 |
added 177 characters in body
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| Mar 27, 2023 at 3:38 | comment | added | Hanul Jeon | @FarmerS Yes. This is what I meant. | |
| Mar 27, 2023 at 2:28 | answer | added | Farmer S | timeline score: 7 | |
| Mar 27, 2023 at 1:41 | comment | added | Farmer S | By "$\Gamma$-Foundation", do you mean the scheme where for every $\Gamma$ formula $\varphi$, we have the axiom that says "For every $p$, if for every $x$, we have $\Big(\forall y\in x\ \varphi(p,y)\Big)\implies\varphi(p,x)$, then for every $x$, we have $\varphi(p,x)$"? | |
| Mar 25, 2023 at 22:44 | history | asked | Hanul Jeon | CC BY-SA 4.0 |