6 papers
Lie methods for countably categorical Engel groups: the Wilson conjecture for -Engel -groups
Christian d'Elbée
In this paper, we are interested in the following conjecture of Wilson from 1981: every locally nilpotent countably categorical group is nilpotent. Following our previous work on t…
A two-sorted theory of nilpotent Lie algebras
Christian d'Elbée, Isabel Müller, Nicholas Ramsey +1
We prove the existence of a model companion of the two-sorted theory of -nilpotent Lie algebras over a field satisfying a given theory of fields. We describe a language in which…
Axiomatic Theory of Independence Relations in Model Theory
Christian d'Elbée
This course introduces the fruitful links between model theory and a combinatoric of sets given by independence relations. An independence relation on a set is a ternary relation b…
Generic multiplicative endomorphism of a field
Christian d'Elbée
We introduce the model-companion of the theory of fields expanded by a unary function for a multiplicative map, which we call ACFH. Among others, we prove that this theory is NSOP$…
Wilson conjecture for omega-categorical Lie algebras, the case 3-Engel characteristic 5
Christian d'Elbée
We prove a version of the Wilson conjecture for -categorical -Engel Lie algebras over a field of characteristic : every -categorical Lie algebra over w…
Wilson conjecture for omega-categorical Lie algebras, the case 4-Engel characteristic 3
Christian d'Elbée
We continue our study of the Wilson conjecture for -categorical Lie algebras and prove that -categorical -Engel Lie algebras of characteristic are nilpotent. We deve…