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Re: TRUE and FALSE values in the relational lattice

From: Jan Hidders <hidders_at_gmail.com>
Date: Fri, 22 Jun 2007 12:10:05 -0000
Message-ID: <1182514205.199556.158650@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.

Received on Fri Jun 22 2007 - 07:10:05 CDT

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