Computable completely decomposable groups
Rodney G. Downey, Alexander Melnikov · Transactions of the American Mathematical Society · 2014
A completely decomposable group is an abelian group of the form ⨁ i H i \bigoplus _i H_i , where H i ≤ ( Q , + ) H_i \leq (Q,+) . We show that every computable completely decomposable group is Δ 5 0 \Delta ^0_5 -categorical. We construct a computable completely decomposable group which is not Δ 4 0 \Delta ^0_4 -categorical, and give an example of a computable completely decomposable group G G which is Δ 4 0 \Delta ^0_4 -categorical but not Δ 3 0 \Delta ^0_3 -categorical. We also prove that the index set of computable completely decomposable groups is arithmetical.