We construct an example of a constructivizable, but not 0′″-autostable, Abelian group of type 2 whose divisible part has dimension 1.
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Yu. L. Ershov and S. S. Goncharov, Constructive Models [in Russian], Nauch. Kniga, Novosibirsk (1999).
A. G. Kurosh, Group Theory [in Russian], Nauka, Moscow (1967).
H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967).
R. I. Soare, Recursively Enumerable Sets and Degrees, A Study of Computable Functions and Computably Generated Sets, Springer, Berlin (1987).
S. S. Goncharov and V. D. Dzgoev, “Autostability of models,” Algebra Logika, 19, No. 1, 45–58 (1980).
R. L. Smith, “Two theorems on autostability in p-groups,” in Lect. Notes Math., 859 (1981), pp. 302–311.
C. J. Ash, “Stability of recursive structures in arithmetical degrees,” Ann. Pure Appl. Log., 32, No. 2, 113–135 (1986).
S. Lempp, Ch. McCoy, R. Miller, and R. Solomon, “Computable categoricity of trees of finite height,” J. Symb. Log., 70, No. 1, 151–215 (2005).
D. I. Dushenin, “Relative autostability of direct sums of Abelian p-groups,” Vestnik NGU, Mat., Mekh., Inf., 10, No. 1, 29–39 (2010).
D. I. Dushenin, “Arithmetical isomorphisms of Abelian p-groups,” Vestnik NGU, Mat., Mekh., Inf., 13, No. 1, 47–56 (2013).
E. Barker, “Back and forth relations for reduced Abelian p-groups,” Ann. Pure Appl. Log., 75, No. 3, 223–249 (1995).
W. Calvert, D. Cenzer, V. S. Harizanov, and A. Morozov, “Effective categoricity of Abelian p-groups,” Ann. Pure Appl. Log., 159, Nos. 1/2, 187–197 (2009).
L. A. Rogers, “Ulm’s theorem for partially ordered structures related to simply presented Abelian p-groups,” Trans. Am. Math. Soc., 227, 333–343 (1977).
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*Supported by the Grants Council (under RF President) for State Aid of Leading Scientific Schools, grant NSh-276.2012.1.
Translated from Algebra i Logika, Vol. 52, No. 4, pp. 403-415, July-August, 2013.
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Dushenin, D.I. Abelian p-groups and autostability relative to an oracle. Algebra Logic 52, 269–276 (2013). https://doi.org/10.1007/s10469-013-9241-x
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DOI: https://doi.org/10.1007/s10469-013-9241-x