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math.LO2025

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…

math.LO2025

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…

math.LO2025

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…

math.LO2024

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…

math.LO2024

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…