On Almost Orthogonality in Simple Theories

Journal of Symbolic Logic 69 (2):398 - 408 (2004)
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1. We show that if p is a real type which is internal in a set $\sigma$ of partial types in a simple theory, then there is a type p' interbounded with p, which is finitely generated over $\sigma$ , and possesses a fundamental system of solutions relative to $\sigma$ . 2. If p is a possibly hyperimaginary Lascar strong type, almost \sigma-internal$ , but almost orthogonal to $\sigma^{\omega}$ , then there is a canonical non-trivial almost hyperdefinable polygroup which multi-acts on p while fixing $\sigma$ generically. In case p is $\sigma-internal$ and T is stable, this is the binding group of p over \sigma$



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Constructing an almost hyperdefinable group.Itay Ben-Yaacov, Ivan Tomašić & Frank O. Wagner - 2004 - Journal of Mathematical Logic 4 (02):181-212.
Imaginaries in pairs of algebraically closed fields.Anand Pillay - 2007 - Annals of Pure and Applied Logic 146 (1):13-20.

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On the fine structure of the polygroup blow-up.Itay Ben-Yaacov - 2003 - Archive for Mathematical Logic 42 (7):649-663.

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