On the Elementary Theory of Restricted Real and Imaginary Parts of Holomorphic Functions

Notre Dame Journal of Formal Logic 53 (1):67-77 (2012)
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Abstract

We show that the ordered field of real numbers with restricted $\mathbb{R}_{\mathscr{H}}$-definable analytic functions admits quantifier elimination if we add a function symbol $^{-1}$ for the function $x\mapsto \frac{1}{x}$ (with $0^{-1}=0$ by convention), where $\mathbb{R}_{\mathscr{H}}$ is the real field augmented by the functions in the family $\mathscr{H}$ of restricted parts (real and imaginary) of holomorphic functions which satisfies certain conditions. Further, with another condition on $\mathscr{H}$ we show that the structure ($\mathbb{R}_{\mathscr{H}}$, constants) is strongly model complete

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Citations of this work

Surreal ordered exponential fields.Philip Ehrlich & Elliot Kaplan - 2021 - Journal of Symbolic Logic 86 (3):1066-1115.

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References found in this work

On the Elementary Theory of Restricted Elementary Functions.Lou van den Dries - 1988 - Journal of Symbolic Logic 53 (3):796 - 808.

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