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Constructive Abelian \(p\)-groups. (English. Russian original) Zbl 0854.03037
Sib. Adv. Math. 2, No. 2, 68-113 (1992); translation from Tr. Inst. Mat. SO RAN 25, 155-199 (1993).
The author finds a necessary and sufficient condition for a countable abelian \(p\)-group which is not the direct sum of cyclic and quasi-cyclic groups to be (strongly) constructivizable. This gives also a condition for an abelian \(p\)-group whose reduced part has finite Ulm type to be (strongly) constructivizable. Every finite direct power of such a group \(G\) is (strongly) constructivizable iff \(G\) is (strongly) constructivizable.

MSC:
03C57 Computable structure theory, computable model theory
20K10 Torsion groups, primary groups and generalized primary groups
03D45 Theory of numerations, effectively presented structures
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