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Journal of Algebra
We study effective categoricity of computable abelian groups of the form i∈ω H, where H is a subgroup of (Q , +). Such groups are called homogeneous completely decomposable. It is well-known that a homogeneous completely decomposable group is computably categorical if and only if its rank is finite. We study 0 n -categoricity in this class of groups, for n > 1. We introduce a new algebraic concept of S-independence which is a generalization of the well-known notion of p-independence. We developdoi:10.1016/j.jalgebra.2012.09.020 fatcat:fr5ae4mhkzhlla66zchc2sz4cq