10 citations · 17 across the 9 of their papers we have counts for
10 papers
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…
On the density of strongly minimal algebraic vector fields
Rémi Jaoui
Two theorems witnessing the abundance of geometrically trivial strongly minimal autonomous differential equations of arbitrary order are shown. The first one states that a generic…
Abelian reduction in differential-algebraic and bimeromorphic geometry
Rémi Jaoui, Rahim Moosa
A new tool for the model theory of differentially closed fields and of compact complex manifolds is here developed. In such settings, it is shown that a type internal to the field…
The degree of nonminimality is at most two
James Freitag, Rémi Jaoui, Rahim Moosa
It is shown that if is a complete type of Lascar rank at least 2 over , in the theory of differentially closed fields of characteristic zero, then there exists a pair of rea…
On the equations of Poizat and Liénard
James Freitag, Rémi Jaoui, David Marker +1
We study the structure of the solution sets in universal differential fields of certain differential equations of order two, the Poizat equations, which are particular cases of Lié…
When any three solutions are independent
James Freitag, Rémi Jaoui, Rahim Moosa
Given an algebraic differential equation of order greater than one, it is shown that if there is any nontrivial algebraic relation amongst any number of distinct nonalgebraic solut…
Relative internality and definable fibrations
Rémi Jaoui, Léo Jimenez, Anand Pillay
We first elaborate on the theory of relative internality in stable theories, focusing on the notion of uniform relative internality (called collapse of the groupoid in an earlier w…
Generic planar algebraic vector fields are disintegrated
Rémi Jaoui
In this article, we study model-theoretic properties of algebraic differential equations of order , defined over constant differential fields. In particular, we show that the se…
Rational factors, invariant foliations and algebraic disintegration of compact mixing Anosov flow of dimension
Rémi Jaoui
In this article, we develop a geometric framework to study the notion of semi-minimality for the generic type of a smooth autonomous differential equation , based on the stu…
Differential fields and Geodesic flows II : Geodesic flows of pseudo-Riemannian algebraic varieties
Remi Jaoui
We define the notion of a smooth pseudo-Riemannian algebraic variety over a field of characteristic , which is an algebraic analogue of the notion of Riemannian mani…