Timeline for Is ordinal definability in terms of stages of cumulative size hierarchy equivalent to the usual one?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 9, 2023 at 13:43 | vote | accept | Zuhair Al-Johar | ||
| Jan 9, 2023 at 11:28 | comment | added | Joel David Hamkins | Ah, in that case, I have posted an answer | |
| Jan 9, 2023 at 11:28 | answer | added | Joel David Hamkins | timeline score: 7 | |
| Jan 9, 2023 at 10:38 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 9, 2023 at 10:35 | comment | added | Zuhair Al-Johar | @JoelDavidHamkins, actually it is the last statement in your comment that I wanted to be sure of! Why it is so? Is that limited to when the base theory is ZF? Or it can work in ZF-Reg. +H_k exists for every set. I mean given any model of ZF-Reg. +H_k, would it satisfy HOD=HOD*? I've changed the notation to avoid confusion. | |
| Jan 9, 2023 at 10:29 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 8, 2023 at 22:42 | comment | added | Joel David Hamkins | This is not what is usually meant by $H_\kappa$, which is defined for cardinals $\kappa$. Your hierarchy is a strange mix of $V_\alpha$ and what would usually be described as $H_{\beth_\alpha}$ (except shifted by $\omega$). Is there a reason to have a different hierarchy? In general, any continuous transfinite hierarchy unioning to $V$ will work equivalently for HOD, since the definitions reflect to any hierarchy. | |
| Jan 8, 2023 at 22:26 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Jan 8, 2023 at 22:12 | history | asked | Zuhair Al-Johar | CC BY-SA 4.0 |