# Re: completeness of the relational lattice

Date: Tue, 26 Jun 2007 15:21:16 -0000

Message-ID: <1182871276.426116.166490_at_q75g2000hsh.googlegroups.com>

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