On almost orthogonality in simple theories

Abstract

1. We show that if p is a real type which is internal in a set Σ of partial types in a simple theory, then there is a type p’ interbounded with p, which is finitely generated over Σ, and possesses a fundamental system of solutions relative to Σ.

2. If p is a possibly hyperimaginary Lascar strong type, almost Σ-internal, but almost orthogonal to Σ^ω, then there is a canonical non-trivial almost hyperdefinable polygroup which multi-acts on p while fixing Σ generically. In case p is Σ-internal and T is stable, this is the binding group of p over Σ.