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Autostability of models and Abelian groups. (English. Russian original) Zbl 0468.03022
Algebra Logic 19, 13-27 (1980); translation from Algebra Logika 19, 23-44 (1980).

MSC:
03D45 Theory of numerations, effectively presented structures
03C15 Model theory of denumerable and separable structures
20K99 Abelian groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20A15 Applications of logic to group theory
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References:
[1] S. S. Goncharov, ”Autostability and computable families of constructivizations,” Algebra Logika,14, No. 6, 647–680 (1975).
[2] S. S. Goncharov, ”On the number of nonautoequivalent constructivizations,” Algebra Logika,16, No. 3, 257–282 (1977).
[3] S. S. Goncharov, ”Constructive Boolean algebras,” in: Third All-Union Conf. on Mathematical Logic [in Russian], Novosibirsk (1974). · Zbl 0281.02049
[4] S. S. Goncharov and V. P. Dobritsa, ”An example of a constructive Abelian group with a nonconstructivizable reduced subgroup,” in: Fourth All-Union Conf. on Mathematical Logic [in Russian], Kishinev (1976). · Zbl 0603.20049
[5] S. S. Goncharov, ”Nonautoequivalent constructivizations of atomic Boolean algebras,” Mat. Zametki,19, No. 6, 853–858 (1976).
[6] Yu. L. Ershov, Theory of Numerations [in Russian], Part. III, Novosibirsk State Univ. (1974).
[7] A. G. Kurosh, Group Theory, Chelsea Publ.
[8] A. I. Mal’tsev, ”On recursive Abelian groups,” Dokl. Akad. Nauk SSSR,146, No. 5, 1009–1012 (1961).
[9] A. T. Nurtazin, ”Computable classes and algebraic conditions for autostability,” Author’s Abstract of Doctoral Dissertation, Novosibirsk (1974).
[10] A. T. Nurtazin, ”Strong and weak constructivizations,” Algebra Logika,13, No. 3, 311–323 (1974).
[11] H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill (1967). · Zbl 0183.01401
[12] S. S. Goncharov and V. D. Dzgoev, ”Autostability of models,” Algebra Logika,19, No. 1, 45–58 (1980). · Zbl 0468.03023
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