The theory of liouville functions

Journal of Symbolic Logic 68 (2):353-365 (2003)
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Abstract

A Liouville function is an analytic function $H : C \rightarrow C$ with a Taylor series $\Sigma_{n=1}^\infty x^n/a_n$ such the $a_n\prime s$ form a "very fast growing" sequence of integers. In this paper we exhibit the complete first-order theory of the complex field expanded with H

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10.2178/jsl/1052669055

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Citations of this work

Notes on quasiminimality and excellence.John T. Baldwin - 2004 - Bulletin of Symbolic Logic 10 (3):334-366.
Model theory of analytic functions: some historical comments.Deirdre Haskell - 2012 - Bulletin of Symbolic Logic 18 (3):368-381.
An Analytic Zariski Structure Over a Field.Nick Peatfield - 2006 - Archive for Mathematical Logic 45 (6):739-768.

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