A Note on the Axioms for Zilber%26apos;s Pseudo-Exponential Fields

作者：Kirby Jonathan^*

来源：Notre Dame Journal of Formal Logic, 2013, 54(3-4): 509-520.

DOI：10.1215/00294527-2143844

• pseudo-exponentiation
• exponential fields
• Schanuel property
• first-order theory
• abstract elementary class

We show that Zilber%26apos;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 class, answering a question of Kesala and Baldwin.

• 出版日期2013