Talk:Generic filter

Untitled

In axiomatic set theory, a discipline within mathematics, a filter F in a poset is called D-generic if

$F\cap E=\varnothing ,\,$ for all E ∈ D

This seems to assume D is some family of subsets of the poset. But it does not say so! Is it just any family? Or some special kind of family? Michael Hardy 00:27, 9 February 2006 (UTC)

I've fleshed out the article quite a bit to address these points. Much more remains to be said.... --Trovatore 02:43, 9 February 2006 (UTC)

Should it be the 'theory' of forcing or the 'method' of forcing? —Preceding unsigned comment added by Chimpionspeak (talk • contribs) 20:45, 8 March 2010 (UTC)

Topology?

The present version of article says:

Now if D is a collection of dense open subsets of P, in the topology whose basic open sets are all sets of the form {q|q≤p} for particular p in P...

I hope I have not overseen something, but I think that in order to get a base, the poset (P,≤) should be directed. --Kompik (talk) 15:11, 16 October 2009 (UTC)