Remarks on unimodulatiry

We clarify and correct some statements and results in the literature concerning unimodularity in the sense of Hrushovski [7], and measur- ability in the sense of Macpherson and Steinhorn [8], pointing out in particular that the two notions coincide for strongly minimal struc- tures and that another property from [7] is strictly weaker, as well as “completing” Elwes’ proof [5] that measurability implies 1-basedness for stable theories

Measurability in Modules

In this paper we prove that in modules, MS-measurability (in the sense of Macpherson-Steinhorn) depends on being able to define a measure function on the p.p. definable subgroups. We give a classification of abelian groups in terms of measurability. Finally we discuss the relation with Q[t]-valued measures

The model theory of Commutative Near Vector Spaces

In this paper we study near vector spaces over a commutative $F$ from a model theoretic point of view. In this context we show regular near vector spaces are in fact vector spaces. We find that near vector spaces are not first order axiomatisable, but that finite block near vector spaces are. In the latter case we establish quantifier elimination, and that the theory is controlled by which elements of the pointwise additive closure of $F$ are automorphisms of the near vector space