Notre Dame Journal of Formal Logic

A Note on the Axioms for Zilber’s Pseudo-Exponential Fields

Jonathan Kirby

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Abstract

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 class, answering a question of Kesälä and Baldwin.

Article information

Source
Notre Dame J. Formal Logic, Volume 54, Number 3-4 (2013), 509-520.

Dates
First available in Project Euclid: 9 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1376053776

Digital Object Identifier
doi:10.1215/00294527-2143844

Mathematical Reviews number (MathSciNet)
MR3091668

Zentralblatt MATH identifier
1345.03070

Subjects
Primary: 03C65: Models of other mathematical theories
Secondary: 03C48: Abstract elementary classes and related topics [See also 03C45]

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

Citation

Kirby, Jonathan. A Note on the Axioms for Zilber’s Pseudo-Exponential Fields. Notre Dame J. Formal Logic 54 (2013), no. 3-4, 509--520. doi:10.1215/00294527-2143844. https://projecteuclid.org/euclid.ndjfl/1376053776


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References

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