  Given a Polish space X and a countable family of analytic hypergraphs on X, I
consider the sigma-ideal generated by Borel sets which are anticliques in at
least one hypergraph in the family. It turns out that many of the quotient
posets are proper. I investigate the forcing properties of these posets,
certain natural operations on them, and prove some related dichotomies. For
this broad class of posets, most fusion arguments and iteration preservation
arguments can be replaced with simple combinatorial considerations concerning
the hypergraphs.
