Definability and definable groups in simple theories
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We continue the study of simple theories begun in [3] and [5]. We first find the right analogue of definability of types. We then develop the theory of generic types and stabilizers for groups definable in simple theories. The general ideology is that the role of formulas (or definability) in stable theories is replaced by partial types (or ∞-definability) in simple theories.
[1] Byunghan Kim. Forking in Simple Unstable Theories , 1998 .
[2] Ehud Hrushovski,et al. Groups definable in local fields and pseudo-finite fields , 1994 .
[3] Saharon Shelah. Simple unstable theories , 1980 .