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

 Messages: [ Previous | Next ]
 Victor Porton Posts: 621 Registered: 8/1/05
Re: Principal Reliods
Posted: Nov 2, 2013 8:10 AM

William Elliot wrote:

> On Fri, 1 Nov 2013, Victor Porton wrote:
>> William Elliot wrote:
>
>> > F_r = F((-r,r)) is a principal filter for R.
>> >
>> > The filter
>> > . . /\_(0<r) F_r = { (a,b) | a < 0 < b } }
>> > is not principal.

>>
>> Right.
>>

>> > Casing this into reloids,
>> > . . /\_(0<r) ({R} xx F_r) = {R} /\ /\_(0<r) F_r

>
>

>> > is the infinum of principal reloids that's not a principal reloid.
>
>> Yes, but if we limit our consideration to principal filters **only**,
>> then by definition any suprema and infima would be also principal.

>
> So you require that only infinums that are principal reloids to be
> accepted? That is not wise for, as shown above, principal reloids would
> not be
> closed under infinite infinums. Thus principal reloids aren't a complete
> lattice.

You wanted to make a quantale out of principal reloids. To make it one need
to restrict suprema and infima only to principal reloids. The resulting
quantale is isomorphic to the quantale of binary relation, so it is
effectively nothing new.

Topic closed.

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