Timeline for No canonical isomorphism
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 23, 2021 at 17:22 | comment | added | Peter LeFanu Lumsdaine | @მამუკაჯიბლაძე: Indeed; to say it another way, there is a natural bijection $\mathrm{Perm}(X) \times \mathrm{Ord}(X) \cong \mathrm{Ord}(X) \times \mathrm{Ord}(X)$. | |
| Apr 23, 2021 at 14:39 | history | edited | LSpice | CC BY-SA 4.0 |
Name of blog post and article
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| Apr 23, 2021 at 13:50 | comment | added | Bertram Arnold | For $X$ infinite, $\operatorname{Perm}(X)$ does not act transitively on the set of well-orderings of $X$ (consider $X = \mathbb N$ with the two well-orderings corresponding to the ordinals $\omega$ and $\omega + 1$). | |
| Apr 23, 2021 at 11:48 | comment | added | მამუკა ჯიბლაძე | A nice example! I believe $\operatorname{Ord}(X)$ has a canonical $\operatorname{Perm}(X)$-torsor structure, no? In fact, $\operatorname{Ord}(X)$ is the set of bijections between the cardinal of $X$ and $X$. So in fact there is a subtlety when $X$ is infinite. Shall one talk about well-orderings in this case? | |
| Apr 23, 2021 at 11:14 | history | edited | Mark Wildon | CC BY-SA 4.0 |
added 21 characters in body
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| S Apr 23, 2021 at 11:07 | history | answered | Mark Wildon | CC BY-SA 4.0 | |
| S Apr 23, 2021 at 11:07 | history | made wiki | Post Made Community Wiki by Mark Wildon |