Timeline for On the role of $\diamondsuit$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 26, 2020 at 16:35 | comment | added | Santi Spadaro | There are various applications of strong diamond principles to the normal vs. collectionwise Hausdorff problem. For example, Shelah proved that under $\Diamond^*$ every normal first-countable space is $\omega_1$-collectionwise Hausdorff. However, I don't know whether the $*$ can be dropped. Paul Szeptycki might know. | |
| Feb 24, 2020 at 0:17 | history | edited | Todd Eisworth | CC BY-SA 4.0 |
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| Feb 23, 2020 at 18:57 | comment | added | Yair Hayut | Baumgartner's result appears in "Order types of real numbers and other uncountable orderings" (MR0661296) and cited also in Moore's paper MR2369944 in which the consistency of CH + no club-minimal Aronszajn trees is proved. Later in Soukup's paper MR4013972, Soukup shows that it is possible to get CH + there is a Suslin tree + no club-minimal Aronszajn trees, and states that the problem of obtaining the club-minimal Aronszajn tree just from diamond is still open. | |
| Feb 23, 2020 at 17:53 | comment | added | Todd Eisworth | Thanks! What's the reference? | |
| Feb 23, 2020 at 13:18 | comment | added | Yair Hayut | Baumgartner proved that $\diamondsuit^+$ implies the existence of a club minimal Aronszajn tree. It is known that CH is not enough and it is open whether $\diamondsuit$ is sufficient. | |
| Feb 22, 2020 at 20:28 | history | asked | Todd Eisworth | CC BY-SA 4.0 |