Computable completely decomposable groups

A completely decomposable group is an abelian group of the form ⊕ i Hi, where Hi ≤ (Q,+). We show that every computable completely decomposable group is Δ5-categorical. We construct a computable completely decomposable group which is not Δ4-categorical, and give an example of a computable completely decomposable group G which is Δ4-categorical but not Δ3-categorical. We also prove that the index set of computable completely decomposable groups is arithmetical.

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