6 citations · 13 across the 14 of their papers we have counts for
17 papers
Lie methods for countably categorical Engel groups: the Wilson conjecture for -Engel -groups
Christian d'Elbée
We are interested in the following conjecture of Wilson from 1981: every locally nilpotent countably categorical group is nilpotent. Following our previous work on the Lie algebra…
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 whi…
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 develo…
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…
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…
Note on a bomb dropped by Mr Conant and Mr Kruckman, and its consequences for the theory ACFG
Christian d'Elbée
This note is a reaction to Conant and Kruckman's recent preprint `Three surprising instance of dividing'. It mainly consists of an erratum to the author's paper `Forking, imaginari…
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 Baudisc…
The Ax-Kochen-Ershov Theorem
Christian d'Elbée
These are the notes of a course for the summer school Model Theory in Bilbao hosted by the Basque Center for Applied Mathematics (BCAM) and the Universidad del País Vasco/Euskal He…
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$…
Vector spaces with a dense-codense generic submodule
Alexander Berenstein, Christian d'Elbée, Evgueni Vassiliev
We study expansions of a vector space over a field , possibly with extra structure, with a generic submodule over a subring of . We construct a natural ex…
Enriching a predicate and tame expansions of the integers
Gabriel Conant, Christian d'Elbée, Yatir Halevi +2
Given a structure and a stably embedded -definable set , we prove tameness preservation results when enriching the induced structure on by some furt…
Existentially closed models of fields with a distinguished submodule
Christian d'Elbée, Itay Kaplan, Leor Neuhauser
This paper deals with the class of existentially closed models of fields with a distinguished submodule (over a fixed subring). In the positive characteristic case, this class is e…
On algebraically closed fields with a distinguished subfield
Christian d'Elbée, Itay Kaplan, Leor Neuhauser
This paper is concerned with the model-theoretic study of pairs where is an algebraically closed field and is a distinguished subfield of allowing extra structu…
Cyclic and non-cyclic division algebras of finite dp-rank
Christian d'Elbée
Milliet asks the following question: given two prime numbers , is there a division algebra of characteristic which is of dp-rank and of dimension over its…
Dp-minimal integral domains
Christian d'Elbée, Yatir Halevi
It is shown that every dp-minimal integral domain is a local ring and for every non-maximal prime ideal of , the localization is a valuatio…
Forking, Imaginaries and other features of ACFG
Christian d'Elbée
We study the generic theory of algebraically closed fields of fixed positive characteristic with a predicate for an additive subgroup, called . This theory was intro…