  We develop a family of simple rank one theories built over quite arbitrary
sequences of finite hypergraphs. (This extends an idea from the recent proof
that Keisler's order has continuum many classes, however, the construction does
not require familiarity with the earlier proof.) We prove a model-completion
and quantifier-elimination result for theories in this family. We develop a
combinatorial property which they share. We invoke regular ultrafilters to show
the strength of this property, showing that any flexible ultrafilter which is
good for the random graph is able to saturate such theories.
