Higher amalgamation properties in stable theories

Abstract

For a complete, stable theory $T$ we construct, in a reasonably canonical way, a related stable theory $T^{\ast }$ which has higher independent amalgamation properties over the algebraic closure of the empty-set. The theory $T^{\ast }$ is an algebraic cover of $T$ and we give an explicit description of the finite covers involved in the construction of $T^{\ast }$ from $T$. This follows an approach of E. Hrushovski. If $T$ is almost strongly minimal with a $0$-definable strongly minimal set, then we show that $T^{\ast }$ has higher amalgamation over any algebraically closed subset.

25 pages