Translator Disclaimer
2012 On the Elementary Theory of Restricted Real and Imaginary Parts of Holomorphic Functions
Hassan Sfouli
Notre Dame J. Formal Logic 53(1): 67-77 (2012). DOI: 10.1215/00294527-1626527

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.

Citation

Download Citation

Hassan Sfouli. "On the Elementary Theory of Restricted Real and Imaginary Parts of Holomorphic Functions." Notre Dame J. Formal Logic 53 (1) 67 - 77, 2012. https://doi.org/10.1215/00294527-1626527

Information

Published: 2012
First available in Project Euclid: 9 May 2012

zbMATH: 1258.03034
MathSciNet: MR2925269
Digital Object Identifier: 10.1215/00294527-1626527

Subjects:
Primary: 03C10
Secondary: 14P15

Rights: Copyright © 2012 University of Notre Dame

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.53 • No. 1 • 2012
Back to Top