7 papers
Shirshov's amalgamated free product and generic nilpotent groups
Christian d'Elbée, Isabel Müller, Nicholas Ramsey +1
In earlier work, the authors gave a construction and description of an amalgamated free product of filtered Lie algebras within a fixed nilpotency class, based on an intricate indu…
The Borovik-Cherlin conjecture holds in ACF
Ulla Karhumäki, Nicholas Ramsey
We show that every faithful, transitive, and generically -transitive action of a connected group on an irreducible variety of dimension , all defined over an…
Measures on bounded perfect PAC fields
Zoé Chatzidakis, Nicholas Ramsey
We describe a construction for producing Keisler measures on bounded perfect PAC fields. As a corollary, we deduce that all groups definable in bounded perfect PAC fields, and even…
Primitive pseudo-finite permutation groups of finite SU-rank
Ulla Karhumäki, Nicholas Ramsey
We study definably primitive pseudo-finite permutation groups of finite -rank. We show that if is such a permutation group, then the rank of can be bounded in terms…
Some model theory of quadratic geometries
Charlotte Kestner, Nicholas Ramsey
Orthogonal spaces are vector spaces together with a quadratic form whose associated bilinear form is non-degenerate. Over fields of characteristic two, there are many quadratic for…
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…
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…