On Quasiminimal Excellent Classes

Abstract

A careful exposition of Zilber's quasiminimal excellent classes and their categoricity is given, leading to two new results: the L_w1,w(Q)-definability assumption may be dropped, and each class is determined by its model of dimension aleph_0.

16 pages. v3: correction to the statement of corollary 5.7

Cited by in corpus (22)

• Shelah's eventual categoricity conjecture in universal classes: part I
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• Finitely Presented Exponential Fields
• A note on the axioms for Zilber's pseudo-exponential fields
• Universal classes near ${\aleph }_1$
• Excellence and uncountable categoricity of Zilber's exponential fields
• The algebraic numbers definable in various exponential fields
• Blurred Complex Exponentiation
• Quasiminimal abstract elementary classes
• Categoricity and covering spaces
• The Γ-Ultraproduct and Averageable Classes
• Structural Logic and Abstract Elementary Classes with Intersection
• Categoricity of modular and Shimura curves
• Finding groups in Zariski-like structures
• Henkin constructions of models with size continuum
• Zilber's notion of logically perfect structure: Universal Covers
• Categoricity of Shimura Varieties
• Quasiminimality of complex powers
• Algebraic types in Zilber's exponential field