Timeline for Introducing meets while preserving directed closure
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 29, 2015 at 0:34 | vote | accept | Sean Cox | ||
| May 28, 2015 at 23:52 | answer | added | Joel David Hamkins | timeline score: 8 | |
| May 28, 2015 at 22:00 | comment | added | Ashutosh | On Sh1036: I proof-read the current arxiv version (part of my job), and requested Shelah to make some changes. They should appear soon. I forgot to say that well-met condition does matter (forcing-wise). Assaf explains this well on his blogpost. | |
| May 28, 2015 at 21:57 | comment | added | Joel David Hamkins | @AsafKaragila I'm not sure. I don't know of any arguments like that. | |
| May 28, 2015 at 21:39 | comment | added | Ashutosh | These could be relevant: Sh1036 and Assaf's blogpost blog.assafrinot.com/?p=3841 | |
| May 28, 2015 at 21:36 | comment | added | Asaf Karagila♦ | @Joel: Is it possible to characterize these sort of failures? Namely, "if $A\subseteq\mathcal B(\Bbb P)$ is a counterexample to some closure property of $\Bbb P$, then ..." or something like that? | |
| May 28, 2015 at 21:15 | comment | added | Noah Schweber | Ah, quite right - that's clear in retrospect, I'm tired today. | |
| May 28, 2015 at 21:11 | comment | added | Joel David Hamkins | @NoahSchweber No infinite complete Boolean algebra is even countably closed, since there must be countably infinite antichains, and you can make an $\omega$-descending sequence by joining the tail starting further and further out. These meet to zero, so the algebra is not countably closed. | |
| May 28, 2015 at 21:08 | comment | added | Noah Schweber | Can you explain how the Boolean closure messes up $\lambda$-directed closedness? I'm not seeing it . . . | |
| May 28, 2015 at 20:55 | comment | added | Asaf Karagila♦ | It sounds weird that Boolean completions can screw up closure properties. | |
| May 28, 2015 at 20:46 | history | asked | Sean Cox | CC BY-SA 3.0 |