Re: Complete axiomatization of relational algebra

Wolfgang Schoenfeld wrote:
> Relational algebra as I understand it is equivalent to first-order
> logic (i.e. there is a transformation - in both directions - which
> preserves validity). Since the set of valid first-order sentences is
> recursively enumerable, the same applies to relational algebra.
>
> But I presume your question is: Is there a finite axiom system for
> relational algebra?

Yes, that is correct.

> I do not know an answer to this, but I remember the corresponding
> question was open for the algebra of BINARY relations. And it was
> answered negatively, i.e. they is no finite equational axiom system.

It depends of course on what type of operations you have in your algebra. If they have for instance something higher order like the transitive closure then this does not imply that there is no finite axiomatization of relational algebra. Could you perhaps give me a reference to some paper that discusses this?

Anyway, thank you for your reaction.

-- 
  Jan Hidders