Timeline for For what sets $X$ do there exist a pair of functions from $X$ to $X$ with the identity being the only function that commutes with both?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Dec 2, 2021 at 22:52 | comment | added | Gro-Tsen | I took the liberty to add references to the result by Sierpiński and Banach (which I did not know). | |
| Dec 2, 2021 at 22:52 | history | edited | Gro-Tsen | CC BY-SA 4.0 |
insert references for the Sierpiński-Banach result (which I did not know)
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| Dec 2, 2021 at 13:46 | history | edited | YCor | CC BY-SA 4.0 |
updated
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| May 8, 2020 at 8:31 | comment | added | YCor | I used above the existence of a strongly rigid binary relation on every set (in ZFC). Let me mention that Hamkins–Palumbo proved that it is consistent with ZF that there exists a set with no rigid binary relation, that is, in which every binary relation has a nontrivial automorphism group, see this post. | |
| May 7, 2020 at 19:09 | comment | added | YCor | Eventually I made it a separate question: mathoverflow.net/questions/359660 | |
| Apr 28, 2020 at 10:40 | comment | added | YCor | One related question I couldn't answer so far is whether there exists $f\in X^X$ whose centralizer is reduced to $\{f^n:n\ge 0\}$. Or if at the opposite, is it true that for $|X|>c$ every $f\in X^X$ has a centralizer cardinal $2^{|X|}$. | |
| Apr 21, 2020 at 1:24 | vote | accept | cha21 | ||
| Apr 20, 2020 at 22:20 | history | edited | YCor | CC BY-SA 4.0 |
added 4 characters in body
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| Apr 20, 2020 at 22:13 | history | answered | YCor | CC BY-SA 4.0 |