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    On Quasiminimal Excellent Classes.Jonathan Kirby - 2010 - Journal of Symbolic Logic 75 (2):551-564.
    A careful exposition of Zilber's quasiminimal excellent classes and their categoricity is given, leading to two new results: the L ω₁ ,ω (Q)-definability assumption may be dropped, and each class is determined by its model of dimension $\aleph _{0}$.
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  2.  22
    A Note on the Axioms for Zilber’s Pseudo-Exponential Fields.Jonathan Kirby - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):509-520.
    We show that Zilber’s conjecture that complex exponentiation is isomorphic to his pseudo-exponentiation follows from the a priori simpler conjecture that they are elementarily equivalent. An analysis of the first-order types in pseudo-exponentiation leads to a description of the elementary embeddings, and the result that pseudo-exponential fields are precisely the models of their common first-order theory which are atomic over exponential transcendence bases. We also show that the class of all pseudo-exponential fields is an example of a nonfinitary abstract elementary (...)
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