Abstract

This paper discusses two combinatorial problems in stability theory. First we prove a partition result for subsets of stable models: for any A and B, we can partition A into |B|$^{ |B|, then we try to find A' $\subset$ A and B' $\subset$ B such that |A'| is as large as possible, |B'| is as small as possible, and A' $\&2ADD;$ $\underset{B'}$ B. We prove some positive results in this direction, and we discuss the optimality of these results under ZFC + GCH.