
Re: Principal Reliods
Posted:
Nov 5, 2013 12:31 AM


On Mon, 4 Nov 2013, Victor Porton wrote: > William Elliot wrote: > > > F_A = pricnipal filter for S generated by {A} (A subset S). > > F(C) = the filter for S generated by C subset P(S). > > > > Theorem. If for all j in J, Aj subset S, then /\_j F_Aj = F_(\/_j Aj), > > The interseciton of principal filters is a principal filter. > > > > Do you already have a proof for that theorem? > > It's a one, or at most, two line proof. > > In my book: > > Corollary 4.86. \uparrow is an order embedding from Z to P. > > (Here Z is a set and P is the corresponding set of principal filter.) There is no such in my copy.
As for Conjecture 4.153, obviously no, a filter cannot be partitioned into ultrafilters because all the ultrafilters contain the same top element.
Do you mean this instead?
If F is a filter for S, can F be partitioned into ultrafilters for subsets of S?

