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Noetherian Zariski structures are introduced by Hrushovski and Zilber(1996). An analytic Zariski structure is a generalization of Noetherian Zariski structures, introduced by Zilber and Peatfield.

For more details you can see the following interesting papers:

1) Zariski Geometries, Zilber and Hrushovski.

2) Analytic Zariski structures and the Hrushovski construction, Peatfield and Zilber.

Question : Under what conditions an analytic Zariski structure is stable ?

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