Re: completeness of the relational lattice

On 25 jun, 22:56, Jan Hidders <hidd..._at_gmail.com> wrote:
>
>
> By the way, I may also some other good news. I looked briefly at the
> problem of the infinitely wide relations, and it seems that is not so
> difficult to solve. The reason is that any expression r that returns
> an infinitely wide result can be rewritten to r' * W where W is my
> version of 11, (W as in "wide" and omega) with r' an expression
> without W. Since for such expressions s' * W and r' * W it holds that
> they are equivalent iff s' and r' are equivalent, this means that we
> can reduce this problem to deciding equivalence for the finitely wide
> expressions. I actually only needed one extra axiom for this:
>
> (32) W + [x] = <x> with x a single attribute

A small correction here. After checking the completeness proof I noticed it was not completely correct. In fact I had needed the following axioms:

(32a)  W + [] = {()}
(32b)  W + [x] = <x>   with x a single attribute
(32c)  [H] * W = [] * W

• Jan Hidders