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A unified approach to constructive and recursive analysis

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Computation and Proof Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1104))

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References

  1. ABERTH, O.: Computable analysis, Mc Graw-Hill, New York, 1980.

    MATH  Google Scholar 

  2. BISHOP, E.: Foundations of constructive analysis, Mc Graw-Hill, New York, 1967.

    MATH  Google Scholar 

  3. BRIDGES, D.S.: Constructive functional analysis, Pitman, London, 1979.

    MATH  Google Scholar 

  4. BROUWER, L.E.J.: Zur Begrūndung der intuitionistischen Mathematik I,II,III, Math. Annalen 93 (1924), 244–258, 95 (1925), 453–473, 96 (1926), 451–489.

    Article  MathSciNet  MATH  Google Scholar 

  5. CEITIN, G.S.: Algorithmic operators in constructive metric spaces. Trudy Mat.Inst.Steklov 67 (1962), 295–361. English translation: Amer. Math. Soc. Trans. (2) 64 (1967), 1–80.

    MathSciNet  Google Scholar 

  6. EGLI, H.; CONSTABLE, R.L.: Computability concepts for programming languages semantics, TCS 2 (1976) 133–145.

    Article  MathSciNet  MATH  Google Scholar 

  7. ERSHOV, JU.L.: Theorie der Numerierungen I, Z.f. math. Logic 19 (1973), 289–388.

    Article  MathSciNet  MATH  Google Scholar 

  8. GRZEGORCZYK, A.: On the definition of computable real continuous functions, Fund. Math. 44 (1957), 61–71.

    MathSciNet  MATH  Google Scholar 

  9. KLAUA, D.: Konstruktive Analysis, Deutscher Verlag der Wissenschaften, Berlin, 1961.

    MATH  Google Scholar 

  10. KO, K.; FRIEDMANN, H.: Computational complexity of real functions, TCS 20 (1982) 323–352.

    Article  MathSciNet  MATH  Google Scholar 

  11. KREITZ, C.; WEIHRAUCH, K.: Complexity theory on real numbers and functions, Proc. 6th GI-Conf., Lecture Notes on comp. Sci. 145 (1982) 165–174.

    Article  MATH  Google Scholar 

  12. KREITZ, C.; WEIHRAUCH, K.: Theory of representations (to appear) Towards a theory of representations, Informatik Berichte 40, Fernuniversitāt Hagen (1983).

    Google Scholar 

  13. KREITZ, C.; WEIHRAUCH, K.: Compactness in constructive analysis revisited (to appear).

    Google Scholar 

  14. KUSHNER, B.A.: Lectures on constructive mathematical analysis, Monographs in mathematical logic and foundations of mathematics, Izdat. "Nauka", Moskau, 1973.

    Google Scholar 

  15. LORENZEN, P.: Differential und Integral — eine konstruktive Einführung in die klassische Analysis, Akademische Verlagsgesellschaft, Frankfurt a.M. 1965.

    MATH  Google Scholar 

  16. MAL'CEV, A.I.: Algorithms and recursive functions, Wolters-Noordhoff, Groningen, 1970

    MATH  Google Scholar 

  17. MYHILL, J.; SHEPHERDSON, J.C.: Effective operations on partial recursive functions, Zeitschrift f. math. Logik 1 (1955), 310–317.

    Article  MathSciNet  MATH  Google Scholar 

  18. NERODE, A.: Lecture on "Constructive analysis", 1982 Summer Institute on recursion theory, Cornell University.

    Google Scholar 

  19. POUR-EL, M.B.: RICHARDS, I.: LP-computability in recursive analysis, Technical Report University of Minnesota (1983).

    Google Scholar 

  20. ROGERS, H. jr.: Theory of recursive functions and effective computability, Mc Graw-Hill, New York, 1967.

    MATH  Google Scholar 

  21. SCOTT, D.: Data Types as lattices, SIAM J. Comp. 5 (1976), 522–587.

    Article  MathSciNet  MATH  Google Scholar 

  22. SPREEN, D.: Effective operations in a topological setting,technical report, RWTH Aachen, 1983.

    Google Scholar 

  23. WEIHRAUCH, K.: Type 2 recursion theory (to be published).

    Google Scholar 

  24. WEIHRAUCH, K.; KREITZ, C.: Representations of the real numbers and of the open subsets of the set of real numbers (to appear).

    Google Scholar 

  25. DEIL, T.: Darstellungen und Berechenbarkeit reeller Zahlen, Dissertation, Fernuniversität Hagen, 1983.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik und Informatik Fernuniversität Hagen, D-5800, Hagen

    Christoph Kreitz & Klaus Weihrauch

Authors
  1. Christoph Kreitz
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  2. Klaus Weihrauch
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Editor information

Egon Börger Walter Oberschelp Michael M. Richter Brigitta Schinzel Wolfgang Thomas

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© 1984 Springer-Verlag

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Kreitz, C., Weihrauch, K. (1984). A unified approach to constructive and recursive analysis. In: Börger, E., Oberschelp, W., Richter, M.M., Schinzel, B., Thomas, W. (eds) Computation and Proof Theory. Lecture Notes in Mathematics, vol 1104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099489

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  • DOI: https://doi.org/10.1007/BFb0099489

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13901-0

  • Online ISBN: 978-3-540-39119-7

  • eBook Packages: Springer Book Archive

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