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

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 Victor Porton Posts: 613 Registered: 8/1/05
Re: Principal Reliods
Posted: Nov 5, 2013 8:18 AM

William Elliot wrote:

> 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?

I mean that filter can be partitioned into ultrafilters in the REVERSE
order.

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