Timeline for Can we iteratively reflect on self elementary embeddable stages of the cumulative hierarchy?
Current License: CC BY-SA 4.0
22 events
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| Jan 19, 2023 at 16:51 | vote | accept | Zuhair Al-Johar | ||
| Jan 19, 2023 at 13:42 | answer | added | Holo | timeline score: 3 | |
| Jan 19, 2023 at 13:18 | comment | added | Holo | Zuhair, your edit to your question has change it immensely, I'll add an answer for the edited question but for the future if you have "small edits" like those, ask in the comment of the existing answer and see if the OP of the answer will have an answer or it deserves a different question, you should avoid editing questions as much as possible | |
| Jan 19, 2023 at 12:51 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 19, 2023 at 12:15 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 18, 2023 at 22:01 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 18, 2023 at 21:54 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 18, 2023 at 21:33 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 18, 2023 at 20:13 | comment | added | Zuhair Al-Johar | @Wojowu,Ah! Now I understand what you are speaking about. Yes! you are right. I meant for every ordinal $\alpha$, I've made the correction. Thanks. | |
| Jan 18, 2023 at 20:12 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 18, 2023 at 20:07 | comment | added | Wojowu | If it's defined for all $\alpha$, then what's the point of specifying it is a partial unary function, and then dabbling with $W_\alpha$ meaning it exists for a given $\alpha$? Also, if we are to be overly pedantic like you are trying to be, this also contradicts the first axiom saying it being well-defined implies $\alpha$ is an ordinal. | |
| Jan 18, 2023 at 20:05 | comment | added | Zuhair Al-Johar | @Wojowu, what? I don't understand your question? Of course it means that $W_\alpha$ exists for all $\alpha$. | |
| Jan 18, 2023 at 20:02 | comment | added | Wojowu | It was most definitely not obvious to me what you meant with that. Anyway, doesn't cumulation axiom imply that $W_\alpha$ exists for all $\alpha$? Or is it only meant to apply for $\alpha$ for which $W_\alpha$ is well defined? | |
| Jan 18, 2023 at 19:59 | comment | added | Zuhair Al-Johar | @HanulJeon, I don't think this is a big issue, it is well known approach, you always use it with the $V_\alpha$ stages, the $H_\alpha$ stages, etc.., it is obvious what I'm using. Of course it is well defined symbol. | |
| Jan 18, 2023 at 19:47 | comment | added | Hanul Jeon | You may not like using $W(\alpha)$ instead of $W_\alpha$, yes, that is okay, but could you write "$W_\alpha$ is well-defined" instead of just putting $W_\alpha$ alone? | |
| Jan 18, 2023 at 19:22 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 18, 2023 at 19:09 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 18, 2023 at 19:03 | comment | added | Zuhair Al-Johar | @HanulJeon, yes it means $\alpha$ is in the domain of $W$, it actually means $W(\alpha)$ but I don't like writing it this way. $\phi$ in elementarity axiom does't use $j$. In Reflection axiom, it can use it. | |
| Jan 18, 2023 at 18:58 | comment | added | Hanul Jeon | Also, is there any restriction on $\phi$ in your formulation of Elementarity and Reflection? Formulation of the Elementarity of a Reinhardt embedding usually only considers formulas in which $j$ does not appear. | |
| Jan 18, 2023 at 18:53 | comment | added | Hanul Jeon | I believe several people already pointed it out, but the fact that your notation is non-standard undermines the understandability of your question. You said that $W_\alpha$ is a partial function, then what is the meaning of $W_\alpha$ as a prime formula? (Do you mean $\alpha$ is in a domain of $W$?) | |
| Jan 18, 2023 at 17:49 | answer | added | Holo | timeline score: 6 | |
| Jan 18, 2023 at 13:22 | history | asked | Zuhair Al-Johar | CC BY-SA 4.0 |