Quasiminimal structures and excellence

Abstract

We show that the excellence axiom in the definition of Zilber's quasiminimal excellent classes is redundant, in that it follows from the other axioms. This substantially simplifies a number of categoricity proofs.

Detail added to proof of 5.2; publication info added

References in corpus (3)

• On Quasiminimal Excellent Classes
• Covers of Multiplicative Groups of Algebraically Closed Fields of Arbitrary Characteristic
• Excellence and uncountable categoricity of Zilber's exponential fields

Cited by in corpus (13)

• Exponentially Closed Fields and the Conjecture on Intersections with Tori
• Pseudo-exponential maps, variants, and quasiminimality
• Excellence and uncountable categoricity of Zilber's exponential fields
• Abstract elementary classes stable in ${\aleph }_0$
• Exponential Sums Equations and Tropical Geometry
• Quasiminimal abstract elementary classes
• Categoricity and covering spaces
• Finding groups in Zariski-like structures
• Non-elementary categoricity and projective locally o-minimal classes
• Quasiminimality of complex powers
• Zilber's notion of logically perfect structure: Universal Covers
• Model theory of special subvarieties and Schanuel-type conjectures
• The small index property for homogeneous models in AECs