Talk:Fréchet filter

I cannot see the use of some modifications somebody did here, i.e. the added first phrase "...is an important concept...".
 * If somebody searches "Fréchet filter", (s)he knows that it's a concept of mathematics. If he didn't, the (extremely simple) definition makes clear that its about mathematics.
 * Whether or not it's important, and in what context, is a judgement that should be left to the reader, IMHO. At least, this should go after the definition, not before, and in a separate section ("applications", "further reading", or so).
 * I agree that a "textual" description can be useful as preamble of some rather complicated concept, but here the preamble is more "frightening" than the very simple definition itself.

MFH 01:03, 10 Mar 2005 (UTC)


 * The first sentence was because one had to mention this is a math article. Wikipedia is a big world, it never hurts to have one introductory sentence explaining where we are.


 * To see who makes what changes, check the "history" on top of the page. It is also good to have the articles on your watchlist, and check the "watchlist" from time to time.


 * I should have done that!


 * Feel free to to revert any of my changes, I would however like to keep the "In mathematics" words. Oleg Alexandrov 01:14, 10 Mar 2005 (UTC)


 * Oh, I'm sorry it was again you I "hit"... (this time I certainly overreacted...). Please forgive... you've so much more experience here, I accept all your arguments and leave your intro as and where it is...MFH 01:59, 10 Mar 2005 (UTC)


 * You will become bolder in time, I am sure! :)


 * Again, all people are equal here. I did some humble changes hoping they are making things a bit better; but there is always room for talking. What is bad is when users take it personally and refuse to compromise. Oleg Alexandrov 02:10, 10 Mar 2005 (UTC)

Ultrafilter including the cofinite filter -- identical or isomorphic?
Regarding The Fréchet filter is included in every free filter and an ultrafilter is free if and only if it includes the Fréchet filter, there is a technical hiccup because ultrafilters are defined more generally on posets and Fréchet/cofinite filters more specifically for a power set lattice. Perhaps there is a representation theorem that can make this okay if isomorphism is swapped for equality. I am not very familiar with this stuff yet, so if anyone knows, a fix or comment would be appreciated. Also, "the" of "the cofinite filter" might lose its footing somewhat in that case.? Cheers, Honestrosewater (talk) 00:16, 17 January 2012 (UTC)

"a theorem equivalent to the axiom of choice"
"The existence of free ultrafilters was established by Tarski in 1930, relying on a theorem equivalent to the axiom of choice..."

Is the second half of the quoted passage correct? I do not have the reference available, but if these authors are referring to Tarski's lemma on Ultrafilters, as I recall this is equivalent over ZF to the Boolean Prime Ideal Theorem, which Halpern and Levy proved in 1971 does not imply the axiom of choice.