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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: 524
Registered: 8/1/05
Re: Principal Reliods
Posted: Nov 2, 2013 8:10 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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

>
> (Correction made.)
>

>> > 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
Read Which term to choose?
Victor Porton
10/25/13
Read Re: Which term to choose?
Peter Percival
10/25/13
Read Re: Which term to choose?
fom
10/25/13
Read Re: Which term to choose?
William Elliot
10/26/13
Read Re: Which term to choose?
William Elliot
10/26/13
Read Re: Which term to choose?
Victor Porton
10/26/13
Read Re: Which term to choose?
William Elliot
10/27/13
Read Re: Which term to choose?
Victor Porton
10/27/13
Read Re: Which term to choose?
William Elliot
10/28/13
Read Re: Which term to choose?
Victor Porton
10/29/13
Read Re: Which term to choose?
William Elliot
10/29/13
Read Re: Which term to choose?
Victor Porton
10/30/13
Read Principal Reliods
William Elliot
10/30/13
Read Re: Principal Reliods
Victor Porton
10/30/13
Read Re: Principal Reliods
William Elliot
10/31/13
Read Re: Principal Reliods
Victor Porton
11/1/13
Read Re: Principal Reliods
William Elliot
11/1/13
Read Re: Principal Reliods
Victor Porton
11/1/13
Read Re: Principal Reliods
William Elliot
11/2/13
Read Re: Principal Reliods
Victor Porton
11/2/13
Read Re: Principal Reliods
William Elliot
11/3/13
Read Re: Principal Reliods
Victor Porton
11/3/13
Read Re: Principal Reliods
Victor Porton
11/3/13
Read Re: Principal Reliods
William Elliot
11/4/13
Read Principal Reliods
William Elliot
11/4/13
Read Re: Principal Reliods
Victor Porton
11/5/13
Read Re: Principal Reliods
William Elliot
11/5/13
Read Re: Principal Reliods
Victor Porton
11/6/13
Read Partition of a filter
William Elliot
11/6/13
Read Re: Partition of a filter
Victor Porton
11/6/13
Read Re: Partition of a filter
William Elliot
11/7/13
Read Re: Partition of a filter
Victor Porton
11/7/13
Read Re: Partition of a filter
William Elliot
11/8/13
Read Partition of a filter
William Elliot
11/8/13
Read Re: Partition of a filter
Victor Porton
11/8/13
Read Re: Partition of a filter
William Elliot
11/9/13
Read Re: Partition of a filter
Victor Porton
11/9/13
Read Re: Partition of a filter
William Elliot
11/9/13
Read Re: Partition of a filter
William Elliot
11/9/13
Read Re: Partition of a filter
Victor Porton
10/26/13
Read Re: Which term to choose?
Victor Porton
11/4/13
Read Re: Which term to choose?
aliahmadikram

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