Quasiminimal abstract elementary classes

Archive for Mathematical Logic 57 (3-4):299-315 (2018)

Abstract
We propose the notion of a quasiminimal abstract elementary class. This is an AEC satisfying four semantic conditions: countable Löwenheim–Skolem–Tarski number, existence of a prime model, closure under intersections, and uniqueness of the generic orbital type over every countable model. We exhibit a correspondence between Zilber’s quasiminimal pregeometry classes and quasiminimal AECs: any quasiminimal pregeometry class induces a quasiminimal AEC, and for any quasiminimal AEC there is a natural functorial expansion that induces a quasiminimal pregeometry class. We show in particular that the exchange axiom is redundant in Zilber’s definition of a quasiminimal pregeometry class.
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DOI 10.1007/s00153-017-0570-7
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References found in this work BETA

Shelah's Eventual Categoricity Conjecture in Universal Classes: Part I.Sebastien Vasey - 2017 - Annals of Pure and Applied Logic 168 (9):1609-1642.
On Quasiminimal Excellent Classes.Jonathan Kirby - 2010 - Journal of Symbolic Logic 75 (2):551-564.
Quasiminimal Structures, Groups and Zariski-Like Geometries.Tapani Hyttinen & Kaisa Kangas - 2016 - Annals of Pure and Applied Logic 167 (6):457-505.
Examples of Non-Locality.John T. Baldwin & Saharon Shelah - 2008 - Journal of Symbolic Logic 73 (3):765-782.

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