Re: What is an automorphism of a database instance?

On Jan 9, 3:53 pm, Tegiri Nenashi <TegiriNena..._at_gmail.com> wrote:
> On Jan 9, 3:29 pm, Kira Yamato <kira..._at_earthlink.net> wrote:
>
> > BTW, do we need to impose partial ordering preserved too? Partial
> > ordering defined as
> > A <= B
> > if and only if
> > A = A /\ B.
>
> A = A /\ B
> imply
> f(A) = f(A /\ B)
> which implies
> f(A) = f(A) /\ f(B)
> which in turn imply
> f(A) <= f(B)
>
> AFAIR in lattice theory an order isomorphism is the same as
> isomorphism defined in terms of operations /\ and \/.

Yes. A lattice isomorphism defined in terms of ^ and v is equivalent to one defined in terms of <=. There are two different kinds of homomorphism, though: meet-homomorphism and join-homomorphism.

Marshall Received on Thu Jan 10 2008 - 01:51:03 CET