Timeline for An ultrafilter is a set of subsets containing exactly one element of each finite partition: reference request
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Jul 4, 2011 at 18:11 | comment | added | Tom Leinster | Thanks, Emil. That's pretty close, though it's not a totally trivial disguise, since in Defn 2.9 he doesn't constrain the union of A_1, ..., A_n to be X. Of course there's nothing difficult about the equivalence between the definition I mentioned and the standard one. It's just a matter of finding a reference where someone has actually said it. | |
Jul 4, 2011 at 17:59 | comment | added | Emil Jeřábek | Lemma 2.10 states it both ways, in a slight disguise. | |
Jul 4, 2011 at 17:04 | comment | added | Tom Leinster | Gerald, either I'm not seeing what you're seeing or you're misunderstanding my question. Cor 2.7 of Galvin states that if a set of subsets of X is an ultrafilter, then it satisfies the partitioning property that I mentioned. But it doesn't state the converse - which is the less obvious half. Re Qiaochu's post, see the comments below my question. | |
Jul 4, 2011 at 16:42 | history | answered | Gerald Edgar | CC BY-SA 3.0 |