Timeline for Which fragment of ZF does the class of all hereditarily predicatively definable sets capture?
Current License: CC BY-SA 4.0
9 events
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| Feb 15, 2023 at 20:04 | vote | accept | Zuhair Al-Johar | ||
| Feb 15, 2023 at 14:15 | comment | added | Zuhair Al-Johar | OK! So the maximal fragment of $\sf ZFC$ that $\sf HPD$ can capture (this is recursively axiomatizable) can interpret $\sf Z_2$, but not more. So, according to reverse mathematics, almost all of traditional mathematics can be captured in $\sf HPD$. | |
| Feb 15, 2023 at 14:07 | comment | added | Holo | @ZuhairAl-Johar $(\omega,+1,<)\in HPD$ and $HPD$ sees that $+1$ is injective, $0$ is not in the image and that $\omega$ is closed under $+1$ and that $<$ is well ordering, so yes (but anything after $Z_2$ pretty much falls flat). But note that we don't know whether $Th(HPD)$ is recursively axiomatible, so consistency strength doesn't mean much for now | |
| Feb 15, 2023 at 13:57 | history | edited | Holo | CC BY-SA 4.0 |
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| Feb 15, 2023 at 13:29 | comment | added | Zuhair Al-Johar | I mean its consistency strength, can it interpret second order arithmetic or is it weaker? Can it interpret PA? | |
| Feb 15, 2023 at 12:51 | history | edited | Holo | CC BY-SA 4.0 |
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| Feb 15, 2023 at 11:53 | comment | added | Holo | @ZuhairAl-Johar what exactly do you mean in this context? | |
| Feb 15, 2023 at 10:52 | comment | added | Zuhair Al-Johar | Does it satisfy second order arithmetic? | |
| Feb 15, 2023 at 10:39 | history | answered | Holo | CC BY-SA 4.0 |