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Siberian Mathematical Journal

, Volume 44, Issue 5, pp 821–828 | Cite as

Computable Solutions of Equations over Endomorphisms of Negative Numberings

  • E. F. Combarro
Article
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Abstract

We prove that a broad class of systems of equations have endomorphisms of negative numberings as solutions. Moreover, we prove that if the endomorphisms of a numbering uniformly solve this class of systems of equations and have the separability property then the numbering is negative.

numbering endomorphism computability 

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References

  1. 1.
    Combarro E. F., “On the endomorphisms of positive and negative numberings,” Siberian Adv. in Math., 11, No. 1, 34–44 (2001).Google Scholar
  2. 2.
    Ershov Yu. L., Theory of Numberings [in Russian], Nauka, Moscow (1977).Google Scholar
  3. 3.
    Hamilton A. G., Logic for Mathematicians, Cambridge Univ. Press, Cambridge (1978).Google Scholar
  4. 4.
    Cutland N. J., Computability, Cambridge Univ. Press, Cambridge (1980).Google Scholar
  5. 5.
    Odifreddi P., Classical Recursion Theory. Vol. 1, North-Holland, Amsterdam etc. (1989).Google Scholar
  6. 6.
    Rogers H., Theory of Recursive Functions and Effective Computability, McGraw-Hill Book Comp., New York; St. Louis; San Francisco; Toronto; London; Sydney (1967).Google Scholar
  7. 7.
    Chang C. C. and Keisler H. J., Model Theory, North-Holland, Amsterdam (1998).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • E. F. Combarro
    • 1
  1. 1.University of OviedoSpain

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