Timeline for Is ZFC interpretable in bisimilar ZFC?
Current License: CC BY-SA 4.0
10 events
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| Feb 7, 2023 at 17:59 | comment | added | Zuhair Al-Johar | @HanulJeon, I need to violate Extensionality, that's important. Aczel's AFA actually strengthens Extensionality, Harvey's is done in a weaker logic. Also Dana Scott's approach doesn't allow a proper class of Atoms. Also there are the works of Gandy, Boffa. But, all those though related yet they don't satisfy what I need. | |
| Feb 7, 2023 at 17:54 | comment | added | Hanul Jeon | If understanding bisimulation is the only purpose, I would rather suggest Aczel's Non-well-founded set or Harvey Friedman's interpretation of $\mathsf{ZF}$ to $\mathsf{IZF}$. | |
| Feb 7, 2023 at 11:41 | comment | added | Zuhair Al-Johar | @PaulTaylor Yes. That is the case when the usual Replacement axiom schema is used. But, when Collection is used instead, then it can interpret full ZFC. But, the situation here is different. | |
| Feb 7, 2023 at 8:43 | comment | added | Zuhair Al-Johar | @Hanul Jeon, In reality an approach to NF through bisimulation as an alternative to Extensionality, but I need to understand it first in ZF context, since models of NFU can be retrieved through automorphisms from models of ZF, so I need to make sure that it works in ZF. | |
| Feb 7, 2023 at 4:12 | comment | added | Hanul Jeon | Just for curiosity, what motivates your question? | |
| Feb 6, 2023 at 19:45 | comment | added | Paul Taylor | I'm not a Set Theorist, so don't quote me on this, but I think Dana Scott's 1966 paper on Extensionality showed that ZF without it is provably consistent in Zermelo set theory alone. That is, no! | |
| Feb 5, 2023 at 10:33 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Feb 5, 2023 at 10:14 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Feb 5, 2023 at 9:51 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Feb 5, 2023 at 9:03 | history | asked | Zuhair Al-Johar | CC BY-SA 4.0 |