Re: Can relational alegbra perform bulk operations?
Date: Thu, 1 Oct 2009 17:28:22 -0700 (PDT)
On Oct 2, 1:08 am, Tegiri Nenashi <tegirinena..._at_gmail.com> wrote:
> On Sep 30, 9:17 pm, David BL <davi..._at_iinet.net.au> wrote:
> > Claim: Under ZFC there is no set which is defined as the
> > set of all sets.
> In RM the level of curly brakets nesting never goes higher than two,
> so set theory paradoxes are irrelevant.
Let R(T) be the set of all relations where every attribute has domain T. For any set T, R(T) exists in ZFC (largely by virtue of the axiom of power set).
Let X be the union of R(T) over all possible T. The definition of X involves unrestricted comprehension and I don't think it exists under ZFC. It seems to me one can study R(T) as an algebraic structure - say with the relational lattice operators, and to the extent that T is not specified (but assumed to be a union type big enough to hold all values of interest) it actually can be regarded as an untyped treatment of the RM.
Does this make sense?
I'm not sure how RVAs fit into that picture. I think recursive types should be allowed, but any given relation (value) only involves finite nesting.
> > Claim: The intersection operator is not a binary function
> Isn't a binary operation on powerset boolean algebra?
As I see it, if one has an operator defined on a proper class, one can take a restriction to a domain which is a set (i.e. a subset of the proper class) to make the operator into a function.
Here is a discussion of "proper class":
http://en.wikipedia.org/wiki/Class_(set_theory) Received on Thu Oct 01 2009 - 19:28:22 CDT