Timeline for Can we have such a sequence of external automorphisms?
Current License: CC BY-SA 4.0
7 events
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| Mar 15, 2021 at 18:00 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Mar 15, 2021 at 17:59 | comment | added | Zuhair Al-Johar | from within the theory one cannot discriminate between standard and non-standard ordinals, the distinction is not made withIN a model, it is made outside it, from within the theory the phrase would be "for some ordinal $\alpha$ we have $j(\alpha) < \alpha$", I've written "non-standard" just to make things clearer from the outside. Ok, I'll change the phrasing to clarify this issue. | |
| Mar 15, 2021 at 16:57 | comment | added | Hanul Jeon | You are working with a formal theory, but the distinction is made within a model. Can the difference between standard and non-standard ordinal be described over the first-order language of set theory? | |
| Mar 15, 2021 at 9:37 | comment | added | Zuhair Al-Johar | A standard ordinal is a well founded transitive set of transitive sets. A non-standard ordinal is a transitive set of transitive sets that externally is not well founded but internally the theory thinks it's well founded, i.e. the theory from inside thinks it is an ordinal, but externally speaking it is not an ordinal because it is not well founded, i.e. externally there is a subset of it that is an infinite descending membership chain, but this subset is not captured internally by the theory, like the set of all elements of $\alpha$ that are moved by $j$ (where $\alpha$ is moved by j) | |
| Mar 15, 2021 at 9:27 | comment | added | Hanul Jeon | What is the difference between standard ordinal and non-standard ordinal? I do not see how to differentiate them. | |
| Mar 15, 2021 at 8:30 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
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| Mar 14, 2021 at 19:43 | history | asked | Zuhair Al-Johar | CC BY-SA 4.0 |