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Enumerations and Completely Decomposable Torsion-Free Abelian Groups

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We study possible degree spectra of completely decomposable torsion-free Abelian groups.

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References

  1. Baer, R.: Abelian groups without elements of finite order. Duke Math. J. 3, 68–122 (1937)

    Article  MathSciNet  Google Scholar 

  2. Coles, R., Downey, R., Slaman, T.: Every set has a least jump enumeration. J. Lond. Math. Soc. (2) 62(3), 641–649

  3. Downey, R.: On presentations of algebraic structures. In: Sorbi (ed.) Complexity, Logic and Recursion Theory, pp. 157–205. Marcel Dekker, New York (1997)

    Google Scholar 

  4. Ershov, Y., Goncharov, S.: Constructive Models. Nauchnaya kniga, Novosibirsk (1999)

    MATH  Google Scholar 

  5. Fuchs, L.: Infinite Abelian Groups, vol. II. Academic Press, New York (1973)

    MATH  Google Scholar 

  6. Khisamiev, N.: Constructive Abelian Groups. Handbook of Recursive Mathematics, vol. 139. Elsevier, Amsterdam (1998)

    Google Scholar 

  7. Mal’tsev, A.I.: On recursive Abelian groups. Soviet Math. Dokl. 3

  8. Miller, R.: The Δ 02 -spectrum of a linear order. J. Symb. Log. 66, 470–486 (2001)

    Article  MATH  Google Scholar 

  9. Selman, A.: Arithmetical reducibilities I. Z. Math. Log. Grundlagen Math. 17, 335–370 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  10. Slaman, T.: Relative to any non-recursive set. Proc. Am. Math. Soc. 126, 2117–2122 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  11. Soare, R.I.: Recursively Enumerable Sets and Degrees. Springer, Berlin/Heidelberg (1987)

    Google Scholar 

  12. Wehner, S.: Enumerations, countable structures and Turing degrees. Proc. Am. Math. Soc. 126, 2131–2139 (1998)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Alexander G. Melnikov.

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Partially supported by President grant of Scientific School NSh-4413.2006.1.

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Melnikov, A.G. Enumerations and Completely Decomposable Torsion-Free Abelian Groups. Theory Comput Syst 45, 897–916 (2009). https://doi.org/10.1007/s00224-009-9175-9

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  • DOI: https://doi.org/10.1007/s00224-009-9175-9

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