5 research outputs found
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
Model theory of finite and pseudofinite groups
This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite group theory
Generic multiplicative endomorphism of a field
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 and not simple, that the kernel of the map is a
generic pseudo-finite abelian group. We also prove that if forking satisfies
existence, then ACFH has elimination of imaginaries.Comment: 34 page
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 TeX -valued measures