Timeline for Special infinitary relations and ultrafilters
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 9, 2011 at 19:59 | vote | accept | porton | ||
| Apr 8, 2011 at 15:19 | comment | added | Emil Jeřábek | It does not, products (restricted or otherwise) of filters satisfy the condition automatically. In fact, the second condition fixed an oversight in the first part of my argument: I didn’t notice that I needed the condition (in particular, $S_i\ne\varnothing$ for every $i$) in order to make the restricted product included in $f$ nonempty (otherwise it would be pointless). | |
| Apr 8, 2011 at 14:44 | comment | added | porton | I did an error, I forgot the second condition in the definition of multifuncoids (now added). Happily this does not break the counter-example by Emil Jeřábek. | |
| Apr 8, 2011 at 14:43 | history | edited | porton | CC BY-SA 3.0 |
Added forgotten second condition in the definition of multifuncoids
|
| Apr 7, 2011 at 17:26 | history | edited | porton | CC BY-SA 2.5 |
Cleared the definition of multifuncoid
|
| Apr 7, 2011 at 16:53 | comment | added | Todd Trimble | But I still think Andreas and Emil are kind! :-) | |
| Apr 7, 2011 at 16:52 | comment | added | Todd Trimble | @Daniel, @Emil: perhaps you are right and I was being unfair to porton. I had some difficulty understanding what a multifuncoid was supposed to be at first reading, which is when I clicked on the link. On another more careful reading, I think it is indeed decipherable -- my apologies. | |
| Apr 7, 2011 at 16:41 | comment | added | porton | Oh, sorry, my "additional condition" was too strong and I commented it out. We may make up some other condition if it will be necessary. | |
| Apr 7, 2011 at 16:39 | history | edited | porton | CC BY-SA 2.5 |
Deleted "the additional condition"
|
| Apr 7, 2011 at 16:39 | comment | added | Daniel Litt | (To be fair, I still am in awe of the kindness of both responders, and have upvoted their answers.) | |
| Apr 7, 2011 at 16:37 | comment | added | Emil Jeřábek | I found the question quite self-contained, I certainly didn’t read any porton’s paper. | |
| Apr 7, 2011 at 16:34 | comment | added | Daniel Litt | @Todd Trimble: While I am of course not thrilled by this question, it seems to me that porton does say what a multifuncoid is, in his fourth paragraph. Or are you referring to another unfamiliar term? | |
| Apr 7, 2011 at 16:33 | comment | added | porton | @Andreas Blass: I a little reordered the text of the question. For "the additional condition" it does not matter what are ultrafilters $a_0$ and $a_1$. $A_i$ and $B_i$ in "the additional condition" are completely arbitrary. For your values of $A$ and $B$ "the additional condition" takes the form $f(U;U)\Leftrightarrow f(U;\emptyset) \vee f(\emptyset;U)$. Hopefully this answers your question. If not please ask more specifically. | |
| Apr 7, 2011 at 16:26 | history | edited | porton | CC BY-SA 2.5 |
Little reorder
|
| Apr 7, 2011 at 16:15 | comment | added | Todd Trimble | I am in awe of the kindness of the mathematicians who responded. The question makes no attempt to define the totally unfamiliar terms, save for a link to porton's web page, where the reader has to pick a paper, take a deep breath, and wade into porton's stuff. I don't think the way the question is worded really deserves such kindness. | |
| Apr 7, 2011 at 15:22 | answer | added | Andreas Blass | timeline score: 10 | |
| Apr 7, 2011 at 15:21 | answer | added | Emil Jeřábek | timeline score: 22 | |
| Apr 7, 2011 at 14:31 | comment | added | Andreas Blass |
Is the additional condition formulated correctly? It seems to me that it fails even for the two-element index set $I=\{0,1\}$ when $a_0$ and $a_1$ are ultrafilters. Take $A_0=B_1=U$ and $A_1=B_0=\emptyset$.
|
|
| Apr 7, 2011 at 13:40 | history | edited | porton | CC BY-SA 2.5 |
Little clarification
|
| Apr 7, 2011 at 11:51 | comment | added | porton | I added a possible (guessed) necessary condition. | |
| Apr 7, 2011 at 11:50 | history | edited | porton | CC BY-SA 2.5 |
Again grammar
|
| Apr 7, 2011 at 11:45 | history | asked | porton | CC BY-SA 2.5 |