Timeline for Cardinality of a set of pairwise non-order-isomorphic ultrafilters on $\omega$
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 19, 2017 at 19:56 | vote | accept | Dominic van der Zypen | ||
| Jul 19, 2017 at 18:39 | comment | added | Joseph Van Name | I gave a proof of how a poset isomorphism induces a Rudin-Keisler isomorphism. | |
| Jul 19, 2017 at 18:38 | answer | added | Joseph Van Name | timeline score: 10 | |
| Jul 19, 2017 at 15:46 | comment | added | Emil Jeřábek | Rudin–Keisler equivalence of uniform ultrafilters clearly induces an isomorphism of the two partially ordered sets, but I don’t see why the converse should hold. In fact, I don’t even see why it couldn’t be the case that all nonprincipal ultrafilters on $\omega$ are isomorphic as partial orders. | |
| Jul 19, 2017 at 14:10 | comment | added | Dominic van der Zypen | Oh - the Rudin-Keisler equivalence is just what I needed, thanks! Can you quickly put this into an answer? | |
| Jul 19, 2017 at 13:57 | comment | added | Joseph Van Name | Two ultrafilters $\mathcal{U}_{1},\mathcal{U}_{2}$ on $\omega$ are isomorphic as posets if and only if they are Rudin-Keisler equivalent. There are $2^{2^{\aleph_{0}}}$ different Rudin-Keisler classes of ultrafilters on $\omega$. | |
| Jul 19, 2017 at 13:51 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |