On local definability of holomorphic functions

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Jones, Gareth, Kirby, Jonathan ORCID: https://orcid.org/0000-0003-4031-9107, le Gal, Olivier and Servi, Tamara (2019) On local definability of holomorphic functions. The Quarterly Journal of Mathematics, 70 (4). pp. 1305-1326. ISSN 0033-5606

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Abstract

Given a collection A of holomorphic functions, we consider how to describe all the holomorphic functions locally definable from A. The notion of local definability of holomorphic functions was introduced by Wilkie, who gave a complete description of all functions locally definable from A in the neighbourhood of a generic point. We prove that this description is no longer complete in the neighbourhood of non-generic points. More precisely, we produce three examples of holomorphic functions that suggest that at least three new operations need to be added to Wilkie's description in order to capture local definability in its entirety. The constructions illustrate the interaction between resolution of singularities and definability in the o-minimal setting.

Item Type:	Article
Uncontrolled Keywords:	math.lo,03c64, 14p10
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	23 Oct 2019 13:30
Last Modified:	07 Nov 2024 12:40
URI:	https://ueaeprints.uea.ac.uk/id/eprint/72748
DOI:	10.1093/qmath/haz015

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