Timeline for Does the partition principle imply (DC)?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 10 at 18:04 | comment | added | Dominic van der Zypen | In ZF, we have that $x\leq y$ implies $x \leq^* y$: if $x\neq \emptyset$ and $x\leq y$, fix $a_0\in x$. Let $f:x\to y$ be an injection. Consider the set $\{(b, a): a\in x, b\in y, f(a) = y\}\cup \{(z,a_0): z\in y \setminus \text{im}(f)\}$. This provides a surjection $g:y\to x$, so $x\leq^* y$. - What is open, is whether the implication $x\leq^*y \implies x\leq y$ is a theorem of ZF. | |
| Sep 10 at 12:20 | comment | added | Juan Atacama | @DominicvanderZypen I assume you meant the implication $x \leq y$ implies $x \leq^* y$. | |
| Apr 14, 2022 at 9:37 | comment | added | Dominic van der Zypen | Apologies for a) misusing the "beg" term and b) missing Higasikawa's paper | |
| Apr 13, 2022 at 21:38 | history | became hot network question | |||
| Apr 13, 2022 at 20:57 | comment | added | Asaf Karagila♦ | While we're making remarks, begthequestion.info | |
| Apr 13, 2022 at 20:16 | vote | accept | Dominic van der Zypen | ||
| Apr 13, 2022 at 18:55 | comment | added | Elliot Glazer | It’s not open, WPP (and thus CB*) implies DC, see Higasikawa’s Partition Principles paper. | |
| Apr 13, 2022 at 13:56 | answer | added | Asaf Karagila♦ | timeline score: 8 | |
| Apr 13, 2022 at 13:37 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |