Elimination of Hyperimaginaries

This chapter addresses the issues on elimination of hyperimaginaries. The Lascar topological group of automorphisms and its quotient groups are investigated as well. A theory has elimination of hyperimaginaries if on each complete type, every type-definable equivalence relation is a conjunction of definable equivalence relation. That low (small, resp.) simple theories eliminate bounded (finitary, resp.) hyperimaginaries is shown. The main result by Buechler, Pillay, and Wagner is that any supersimple theory eliminates hyperimaginaries. The result has consequences in regard to the definability and canonical bases of Lascar types.