  We discuss the connection between various orders on the class of all the
ultrafilters and certain compactness properties of abstract logics and of
topological spaces. We present a model theoretical characterization of Comfort
order. We introduce a new order motivated by considerations in abstract model
theory. For each of the above orders, we show that if $E$ is a $(\lambda,
\lambda)$-regular ultrafilter, and $D$ is not $(\lambda, \lambda)$-regular,
then $E \not \leq D$. Many problems are stated.
