826 research outputs found
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 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 are automorphisms of the near
vector space
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