Séminaires : Géométrie et Théorie des Modèles

Liouville introduced the class of elementary functions to study analogues of the notion of resolubility by radicals for algebraic equations for transcendental and differential equations. Can the primitive of an algebraic function be expressed as an elementary function? Is the restricted (real-analytic) cosine function definable in the structure (R,+,x, exp)? Does a planar vector field admits an elementary integral?
In my talk, I will describe how the (omega-stable) theory of blurred exponential fields axiomatized by Kirby around 2007 provide a new framework for the development of model-theoretic techniques to unify and study the various notions of integrability by elementary functions. This is joint work with Jonathan Kirby.