Re: TRUE and FALSE values in the relational lattice
Date: Fri, 22 Jun 2007 12:10:05 -0000
Message-ID: <1182514205.199556.158650_at_q69g2000hsb.googlegroups.com>
On 22 jun, 12:33, Joe Thurbon <use..._at_thurbon.com> wrote:
> Jan Hidders wrote:
>
> [...]
>
>
>
> > Me too. :-) Finding a simple finite algebraic complete axiomatization
> > for FOL is an open problem.
>
> PMFJI, but would a Lindenbaum algebra be the thing you're looking for?
Yes, Lindenbaum-Tarski algebras, as they are also sometimes called. There is a complete axiomatization for propositional logic, but as far as I know there no complete axiomatization of these when they deal with predicate logic. And that is of course what we are dealing with here.
> It's been a while (almost 10 years) since I've done any serious logic,
> and I never used them then anyway, but from memory they are only
> non-finite when the logic in question has a non-finite number of atoms.
Which, I'm affraid, is what we have here. Still, it may be an interesting direction to look, so thanks for mentioning it.
- Jan Hidders