pace of ending.

I think I have a proof that KA^(2K)-periodic

K-uniform sequences in A exist for all A, K.

I still would conjecture that A^K-periodic sequences

exist. A uniform sequence in A can be constructed

out of these, and (K x K)-uniform mappings

\N x \N -> A can be constructed out of K-uniform

sequences in A, and a uniform mapping \N x \N -> A

from those.

Also, if f : X -> Y is K-uniform and L subseteq K

and K \ L finite, then f is L-uniform.

I need some notion of a 'density structure' for

a nice general definition of uniformity, like

a set A, and a set T of monomorphisms A >-> A, and

a filter D on T. (For instance we can take A := \N,

T := { x :-> x + n | n \in \N } and

D := { { x | x \in \N, x > n } | n \in \N }

and get back the usual concept of uniformity

I was dealing with on \N.