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LOCAL INTERDEFINABILITY OF WEIERSTRASS ELLIPTIC FUNCTIONS

Part of: Number theory: Connections with logic Model theory

Published online by Cambridge University Press:  24 November 2014

Gareth Jones ,
Jonathan Kirby  and
Tamara Servi
Gareth Jones
Affiliation:
School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK (gareth.jones-3@manchester.ac.uk)
Jonathan Kirby
Affiliation:
School of Mathematics, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, UK (jonathan.kirby@uea.ac.uk)
Tamara Servi
Affiliation:
Centro de Matemática e Applicações Fundamentais, Av. Prof. Gama Pinto, 2 1649-003, Lisboa, Portugal (tamara.servi@gmail.com)
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Abstract

We explain which Weierstrass ${\wp}$-functions are locally definable from other ${\wp}$-functions and exponentiation in the context of o-minimal structures. The proofs make use of the predimension method from model theory to exploit functional transcendence theorems in a systematic way.

Keywords

o-minimalitylocal definabilityWeierstrass ℘-functionpredimension

MSC classification

Primary: 03C64: Model theory of ordered structures; o-minimality
Secondary: 11U09: Model theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 15 , Issue 4 , October 2016 , pp. 673 - 691
Copyright
© Cambridge University Press 2014 

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