Séminaires : Géométrie et Théorie des Modèles

A few years ago, Rahim Moosa and I introduced the degree of nonminimality, which was designed for proving transcendence statements for solutions of differential equations. We'll spend the first half of the talk developing the notion and describing the applications. The degree of nonminimality is just one way to make quantitative the general model theoretic fact that dividing of any partial type can always be detected by some indiscernible sequence in the parameters of the formulas. In the second half of the talk, we will describe several variations on the notion which have recent applications beyond transcendence results.