
Re: Which term to choose?
Posted:
Oct 28, 2013 8:12 AM


William Elliot wrote:
> On Sun, 27 Oct 2013, Victor Porton wrote: > >> >> > Is this it? Let F be a principal filter for XxY >> >> > and for all j in J, Gj a filter for YxZ. Then >> >> > . . F o /\_j Gj = /\{ F o Gj  j in J }. >> >> > >> >> > Also if F filter for XxY, G,H filter for YxZ, then >> >> > . . F o G/\H = FoG /\ FoH. >> >> >> >> Yes, these two theorems are correct. > >> >> I know no other distributive theorems of reloids. >> > But you said you wrote a whold chapter about that. >> >> I wrote a chapter with the proof that for every principal reloid F >> F o /\_j Gj = /\{ F o Gj  j in J }. >> > Why a whold chapter? The proof is so short and the topic so basic > that it should be included in the basic chapter on reloids. > > Anyway, that shows that principal reliods with composition > are order dual to quantales.
This result is not interesting, because principal reloids are essentially the same as binary relations.
That binary relations with composition are order dual to quantales, isn't a new result.

