Hello
all:

For some time, I
have thought it would be possible to do tame congruence theory for infinite
algebras. There may not be minimal algebras as there are guaranteed to be
with a finite algebra, but there are guaranteed to be minimal _filters_ of
algebras in the lattice of filters. (Note, that to my way of thinking,
filters should be ordered by reverse inclusion, so that an ultrafilter is
minimal, in my opinion.) Is that all that's needed? If minimal
filters of algebras aren't quite the thing, then there are minimal algebra
objects in the category of filters. (There was a classic 1967, or
something, paper with that title.)

If we looked at
these minimal objects, would there still always be 5 kinds of them, or would
there be more? No idea here.

I just wanted to
throw this out there and see if anyone was interested in the idea. I have
basically no free time to work on it.

Bill
Rowan