
Re: Principal Reliods
Posted:
Nov 1, 2013 9:55 PM


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.

