July 21st, 2000

beartato phd


Finished "Snow Crash". Also good, but weird
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.