Timeline for NCF, P-points, weak P-points, and cardinalities
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 20, 2020 at 13:25 | comment | added | Damian Sobota | Will, concerning your last comment, we have two P-points RK-below a P-point. This means that they're RB-below (Rudin-Blass) a P-point, which is equivalent to be RB-above an ultrafilter (Laflamme--Zhu), which then again must be a P-point. This means that they're compatible. | |
| Mar 20, 2020 at 13:04 | comment | added | Will Brian | For the second part of question 5, let me point out that finitely many equivalence classes implies there are non-isomorphic $P$-points. We already know it gives us $P$-points that are not selective. But an ultrafilter is RK-minimal iff it is selective, so there are $P$-points with ultrafilters strictly RK-below them. But anything RK-below a $P$-point is also a $P$-point. | |
| Mar 20, 2020 at 13:04 | comment | added | Damian Sobota | In question 4 I'm asking about weak P-points. | |
| Mar 20, 2020 at 12:48 | history | edited | Will Brian | CC BY-SA 4.0 |
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| Mar 20, 2020 at 12:34 | comment | added | Todd Eisworth | Note that $\mathfrak{u}=\mathfrak{d}=\aleph_1$ in this model, so you have $2^{\mathfrak{c}}$ near coherence classes as well. You didn't ask about this specifically, but it seemed relevant to the spirit of your question. | |
| Mar 20, 2020 at 12:30 | comment | added | Damian Sobota | Thanks, Will! I was pretty sure that I had heard about this result, but couldn't find it in the literature, so started to doubt it... | |
| Mar 20, 2020 at 12:19 | history | answered | Will Brian | CC BY-SA 4.0 |