1.4k citations
- University of East AngliaGB92 papers
- Centre National de la Recherche ScientifiqueFR16 papers
- Max Planck Institute for Radio AstronomyDE11 papers
- Netherlands Institute for Radio AstronomyNL10 papers
- Quadram InstituteGB10 papers
- University of ManchesterGB10 papers
- West Virginia UniversityUS10 papers
- Chinese Academy of SciencesCN9 papers
- Cornell UniversityUS9 papers
- Istituto Nazionale di Fisica Nucleare, Sezione di TorinoIT9 papers
- McGill UniversityCA9 papers
- National Radio Astronomy ObservatoryUS9 papers
11 papers · 1 filter
Integration in finite terms and exponentially algebraic functions
Rémi Jaoui, Jonathan Kirby
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differentia…
Existentially Closed Exponential Fields
Levon Haykazyan, Jonathan Kirby
We characterise the existentially closed models of the theory of exponential fields. They do not form an elementary class, but can be studied using positive logic. We find the amal…
On local definability of holomorphic functions
Gareth Jones, Jonathan Kirby, Olivier Le Gal +1
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 f…
Blurred Complex Exponentiation
Jonathan Kirby
It is shown that the complex field equipped with the "approximate exponential map", defined up to ambiguity from a small group, is quasiminimal: every automorphism-invariant subset…
The rational field is not universally definable in pseudo-exponentiation
Jonathan Kirby
We show that the field of rational numbers is not definable by a universal formula in Zilber's pseudo-exponential field.
Local interdefinability of Weierstrass elliptic functions
Gareth Jones, Jonathan Kirby, Tamara Servi
We explain which Weierstrass elliptic functions are locally definable from other elliptic functions and exponentiation in the context of o-minimal structures. The proofs make use o…