Timeline for Can this Ackermann like set theory formulated without adding a primitive of set-hood reach the consistency of ORD is Mahlo?
Current License: CC BY-SA 4.0
12 events
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| Jan 13, 2021 at 20:54 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 13, 2021 at 6:49 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 13, 2021 at 6:45 | comment | added | Zuhair Al-Johar | @GregKirmayer, for precision purposes, I'll try put a note to that effect. | |
| Jan 12, 2021 at 18:27 | comment | added | Zuhair Al-Johar | @GregKirmayer, I agree, and I know what you mean, but I'm here abusing the notation, and I think its a common abuse and fairly understood, the point is that there will be no $A,B$ symbols when the formula is parameter free, but to write that explicitly it'll be messy that's why I didn't write it. My idea is that when $\phi$ is for example the formula $Y \neq Y$ then the formula $\pi$ would be read without symbols $A,B$ at all, so it'sll be $\forall Y (Y \neq Y \Rightarrow H_{<W}(Y)) \to \exists X < W (X=\emptyset)$, the same thing apply for formula $Y=A$ here $\pi$ would not have $B$ in it. | |
| Jan 12, 2021 at 17:33 | comment | added | Greg Kirmayer | The scheme begins with "∀𝐴,𝐵 𝑎𝑟𝑒 𝐻<𝑊". The whole scheme is true for empty W, because there are no such 𝐴,𝐵. | |
| Jan 12, 2021 at 17:18 | comment | added | Zuhair Al-Johar | $\exists W: W \neq \emptyset$ is a theorem of this theory! Just let $\phi$ be any false formula without parameters and substitute it in Reflection. | |
| Jan 12, 2021 at 17:11 | comment | added | Greg Kirmayer | The reflection scheme always holds. Perhaps you want to add W is not empty. | |
| Jan 12, 2021 at 14:55 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 12, 2021 at 14:48 | history | undeleted | Zuhair Al-Johar | ||
| Jan 12, 2021 at 14:46 | history | deleted | Zuhair Al-Johar | via Vote | |
| Jan 11, 2021 at 13:28 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 11, 2021 at 8:49 | history | asked | Zuhair Al-Johar | CC BY-SA 4.0 |