Re: More on lists and sets

> > Relational lattice theory is not complete. Many parts still remain
> > informal -- Spight distributivity criteria among them. It could be
> > written formally, but this expression
> >
> > (A /\ C /\ 00) \/ (B /\ C /\ 00) \/ (A /\ B /\ 00)
> > = (B /\ 00) \/ (C /\ 00)
> > ==>
> > A /\ (B \/ C) == (A /\ B) \/ (A /\ C)
> >
> > doesn't look like a satisfying axiom.
>
> Understood, but let's start first with a simpeler question. Is the
> axiomatization complete if we only consider /\ and \/? (So no 00, 01,
> 10 and 11.)

Then I don't understand your question. If we remove constant symbols (00 and 11 being the most important ones), then what is left are the lattice axioms. Lattices however are more general than relation algebras. Example: N_5. (Witness that N_5 can't have a header with more than one variable, because all these relation algebras have sublattices of headers with 4 elements. They can't be empty, otherwise they are boolean algebras. If they are nonemty they would have more than 5 elements. The case of one variable is easy to check as well.) Clearly, there are missing laws that have to amend lattice structure in order to describe relational lattice. Received on Wed Mar 29 2006 - 19:59:24 CEST