Date: Nov 4, 2013 5:55 AM
Author: Victor Porton
Subject: Re: Principal Reliods

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.)