Definability patterns and their symmetries

Journal article

We identify a canonical structure J associated to any first-order theory, the {\it space of definability patterns}. It generalizes the imaginary algebraic closure in a stable theory, and the hyperimaginary bounded closure in simple theories. J admits a compact topology, not necessarily Hausdorff, but the Hausdorff part can already be bigger than the Kim-Pillay space. Using it, we obtain simple proofs of a number of results previously obtained using topological dynamics, but working one power ...

Expand abstract

Authors: Hrushovski, E

• Publication status: Not published
• Peer review status: Not peer reviewed
• Keywords: math.LO