Quasiminimal structures and excellence
Martin Bays, Bradd Hart, Tapani Hyttinen, Meeri Kes\"al\"a and, Jonathan Kirby
TL;DR
This paper demonstrates that the excellence axiom in Zilber's quasiminimal excellent classes is redundant, simplifying categoricity proofs by deriving it from other axioms.
Contribution
It proves that the excellence axiom is implied by other axioms, reducing the complexity of the foundational framework for quasiminimal classes.
Findings
Excellence axiom is redundant in quasiminimal classes
Simplifies categoricity proofs
Reduces axiomatic complexity in model theory
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.
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