  Define a set of lines in $R^3$ to be ``stacked'' with respect to $v \in R^3$
if, from a vantage point far away in the direction of $v$, the lines are
linearly ordered by the ``crossing over'' relation. Given a collection of skew
lines and a point $v$, we ask, what is the largest stacked subset that must be
present among the lines? This question, which appears in a 2000 paper of Erdos,
Hajnal and Pach, is intimately related to the well-known Erdos-Hajnal
conjecture via the Milnor-Thom theorem. It was recently resolved by a powerful
and very general theorem of Alon, Pach, Pinchasi, Radoicic, and Sharir. We
describe these results and discuss several related issues, including a
generalization to ``Erdos-Hajnal sets'' and an intriguing problem concerning
the decomposability of semi-algebraic sets: Do all semi-algebraic sets belong
to the set algebra generated by semigroups in $R^d$? Our main result is a
resolution of this question in dimensions 1 and 2.
