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Siberian Mathematical Journal

, Volume 58, Issue 5, pp 794–800 | Cite as

Conditional terms in semantic programming

  • S. S. Goncharov
Article

Abstract

For constructing an enrichment of the language with restricted quantifiers, we extend the construction of conditional terms. We show that the so-obtained extension of the language of formulas with restricted quantifiers over structures with hereditary finite lists is a conservative enrichment.

Keywords

formula term restricted quantifier Δ0-formula Σ-formula semantic programming computability computability over abstract structures conditional term 

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References

  1. 1.
    Goncharov S. S. and Sviridenko D. I., “S-Programming,” Transl. II Ser., Amer. Math. Soc., no. 142, 101–121 (1989).zbMATHGoogle Scholar
  2. 2.
    Goncharov S. S. and Sviridenko D. I., “S-Programming and their semantics,” Vychisl. Systemy, no. 120, 24–51 (1987).zbMATHGoogle Scholar
  3. 3.
    Goncharov S. S. and Sviridenko D. I., “Theoretical aspects of S-programming,” Lect. Notes Comp. Sci., vol. 215, 169–179 (1986).CrossRefzbMATHGoogle Scholar
  4. 4.
    Ershov Yu. L., Goncharov S. S., and Sviridenko D. I., “Semantic programming,” in: Information Processing 86: Proc. IFIP 10th World Comput. Congress. Vol. 10, Elsevier Sci., Dublin, 1986, 1093–1100.zbMATHGoogle Scholar
  5. 5.
    Goncharov S. S. and Sviridenko D. I., “Mathematical bases of semantic programming,” Soviet Math. Dokl., vol. 31, no. 6, 608–610 (1986).zbMATHGoogle Scholar
  6. 6.
    Ershov Yu. L., Goncharov S. S., and Sviridenko D. I., “Semantic foundations of programming,” in: Fundamentals of Computation Theory: Proc. Intern. Conf. FCT 87, Kazan, 1987, 116–122 (Lect. Notes Comp. Sci.; V. 278).CrossRefGoogle Scholar
  7. 7.
    Ershov Yu. L., “The principle of S-enumeration,” Soviet Math. Dokl., vol. 27, 670–672 (1983).zbMATHGoogle Scholar
  8. 8.
    Ershov Yu. L., “Dynamic logic over admissible sets,” Soviet Math. Dokl., vol. 28, 739–742 (1983).zbMATHGoogle Scholar
  9. 9.
    Ershov Yu. L., Definability and Computability, Kluwer Akad./Consultants Bureau (Siberian School of Algebra and Logic), New York (1996).zbMATHGoogle Scholar
  10. 10.
    Goncharov S. S., “The theory of lists and its models,” Vychisl. Systemy, no. 114, 84–95 (1986).zbMATHMathSciNetGoogle Scholar
  11. 11.
    Goncharov S. S., “Remark about axioms of the list superstructure GES,” Vychisl. Systemy, no. 114, 11–15 (1986).zbMATHGoogle Scholar
  12. 12.
    Ershov Yu. L., Goncharov S. S., Nerode A., and Remmel J. B., “Introduction to the Handbook of Recursive Mathematics,” in: Handbook of Recursive Mathematics, Elsevier, Amsterdam etc., 1998. Part 1. V. 1–2. P. vii–xlvi.zbMATHGoogle Scholar
  13. 13.
    Ershov Yu. L., Puzarenko V. G., and Stukachev A. I., “HF-Computability,” in: Computability in Context: Computation and Logic in the Real World, S. B. Cooper and A. Sorbi (eds.), Imperial College Press/World Sci., London, 2011, 169–242.CrossRefGoogle Scholar
  14. 14.
    Morozov A. S. and Puzarenko V. G., “S-subsets of natural numbers,” Algebra and Logic, vol. 43, no. 3, 162–178 (2004).CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Sobolev Institute of Mathematics Novosibirsk State UniversityNovosibirskRussia

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