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Topic: Which term to choose?
Replies: 41   Last Post: Nov 9, 2013 5:20 AM

 Messages: [ Previous | Next ]
 William Elliot Posts: 2,637 Registered: 1/8/12
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.

If F is a filter for S, can F be partitioned
into ultrafilters for subsets of S?

Date Subject Author
10/25/13 Victor Porton
10/25/13 Peter Percival
10/25/13 fom
10/25/13 William Elliot
10/26/13 William Elliot
10/26/13 Victor Porton
10/26/13 William Elliot
10/27/13 Victor Porton
10/27/13 William Elliot
10/28/13 Victor Porton
10/29/13 William Elliot
10/29/13 Victor Porton
10/30/13 William Elliot
10/30/13 Victor Porton
10/30/13 William Elliot
10/31/13 Victor Porton
11/1/13 William Elliot
11/1/13 Victor Porton
11/1/13 William Elliot
11/2/13 Victor Porton
11/2/13 William Elliot
11/3/13 Victor Porton
11/3/13 Victor Porton
11/3/13 William Elliot
11/4/13 William Elliot
11/4/13 Victor Porton
11/5/13 William Elliot
11/5/13 Victor Porton
11/6/13 William Elliot
11/6/13 Victor Porton
11/6/13 William Elliot
11/7/13 Victor Porton
11/7/13 William Elliot
11/8/13 William Elliot
11/8/13 Victor Porton
11/8/13 William Elliot
11/9/13 Victor Porton
11/9/13 William Elliot
11/9/13 William Elliot
11/9/13 Victor Porton
10/26/13 Victor Porton