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Σ-Uniform structures and Σ-functions. I

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Algebra and Logic Aims and scope

The concept of a Σ-uniform structure is introduced. A condition is derived which is necessary and sufficient for a universal Σ-function to exist in a hereditarily finite admissible set over a Σ-uniform structure.

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References

  1. Yu. L. Ershov, Definability and Computability, Sib. School Alg. Log. [in Russian], 2nd ed., Ekonomika, Moscow (2000).

    Google Scholar 

  2. V. A. Rudnev, “A universal recursive function on admissible sets,” Algebra Logika, 25, No. 4, 425–435 (1986).

    Article  MathSciNet  Google Scholar 

  3. A. S. Morozov and V. G. Puzarenko, “Σ-subsets of natural numbers,” Algebra Logika, 43, No. 3, 291–320 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  4. I. Sh. Kalimullin and V. G. Puzarenko, “Computability principles on admissible sets,” Mat. Trudy, 7, No. 2, 35–71 (2004).

    MathSciNet  MATH  Google Scholar 

  5. V. G. Puzarenko, “Toward a computability on special models,” Sib. Mat. Zh., 46, No. 1, 185–208 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. N. Khisamiev, “On Σ-subsets of naturals over abelian groups,” Sib. Mat. Zh., 47, No. 3, 695–706 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. N. Khisamiev, “Σ-bounded algebraic systems and universal functions. I,” Sib. Mat. Zh., 51, No. 1, 217–235 (2010).

    Article  MathSciNet  Google Scholar 

  8. A. N. Khisamiev, “Σ-bounded algebraic systems and universal functions. II,” Sib. Mat. Zh., 51, No. 3, 676–693 (2010).

    Article  MathSciNet  Google Scholar 

  9. A. N. Khisamiev, “Σ-uniform algebraic systems and universal Σ-functions,” Tr. Int. Conf. “Computability and Models”, VKGTU, Ust-Kamenogorsk (2010), pp. 115–130.

    Google Scholar 

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. N. Khisamiev

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  1. A. N. Khisamiev
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Correspondence to A. N. Khisamiev.

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Supported by RFBR (project No. 08-01-00336) and by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-3606.2010.1). (A. N. Khisamiev)

Translated from Algebra i Logika, Vol. 50, No. 5, pp. 659–684, September-October, 2011.

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Khisamiev, A.N. Σ-Uniform structures and Σ-functions. I. Algebra Logic 50, 447–465 (2011). https://doi.org/10.1007/s10469-011-9155-4

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  • DOI: https://doi.org/10.1007/s10469-011-9155-4

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