6 papers · 1 filter
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…
Model-theoretic properties of nilpotent groups and Lie algebras
Christian d'Elbée, Isabel Müller, Nicholas Ramsey +1
We give a systematic study of the model theory of generic nilpotent groups and Lie algebras. We show that the Fraïssé limit of 2-nilpotent groups of exponent studied by Baudi…
The classification of dp-minimal integral domains
Christian d'Elbée, Yatir Halevi, Will Johnson
We classify dp-minimal integral domains, building off the existing classification of dp-minimal fields and dp-minimal valuation rings. We show that if R is a dp-minimal integral do…