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Identity and existence in intuitionistic logic

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Applications of Sheaves

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References

  1. Bishop, E.: Foundations of Constructive Analysis. McGraw-Hill, 1967

    Google Scholar 

  2. Church, A.: A formulation of the simple theory of types. J.S.L. 5, 56–68 (1940)

    MathSciNet  MATH  Google Scholar 

  3. Church, A.: Introduction to Mathematical Logic. Princeton U.P., 1956

    Google Scholar 

  4. Dalen, D. van, Statman, R.: Equality in the presence of apartness. To appear

    Google Scholar 

  5. Diaconescu, R.: Axiom of choice and complementation. Proc. Amer. Math. Soc. 51, 175–178 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dummett, M.: Elements of Intuitionism. Oxford U.P. 1977

    Google Scholar 

  7. Fourman, M.P.: Connections between category theory and logic. D.Phil. thesis: Oxford 1974

    Google Scholar 

  8. Fourman, M.P.: The logic of topoi, in Handbook of Mathematical Logic, (Ed. Barwise, J.). North Holland 1977, 1053–1090

    Google Scholar 

  9. Fourman, M.P., Hyland, J.M.E.: Sheaf models for analysis. This volume

    Google Scholar 

  10. Fourman, M.P., Scott, D.S.: Sheaves and logic. This volume

    Google Scholar 

  11. Gabbay, D.M.: On 2nd order intuitionistic propositional calculus with full comprehension. Archiv für mathematische Logic und Grundlagen-forschung, 16, 177–186 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  12. Gray, J.W.: The meeting of the midwest category seminar in Zurich, August 1970, in Reports of the Midwest Category Seminar V (Ed. Gray, J.W.). Lecture Notes in Mathematics, 195. Berlin and New York: Springer 1971

    Chapter  Google Scholar 

  13. Grayson, R.J.: Heyting-valued models for intuitionistic set theory. This volume

    Google Scholar 

  14. Henkin, L.: Completeness in the theory of types. J.S.L. 15, 81–91 (1950)

    MathSciNet  MATH  Google Scholar 

  15. Henkin, L.: A theory of propositional types. Fund. Math. 52, 323–344 (1963)

    MathSciNet  MATH  Google Scholar 

  16. Johnstone, P.T.: Topos Theory. Academic Press 1977

    Google Scholar 

  17. MacLane, S.: Categories for the Working Mathematician. Springer 1971

    Google Scholar 

  18. Makkai, M., Reyes, G.E.: First-order Categorical Logic. Lecture Notes in Mathematics, 611. Berlin and New York: Springer 1977

    Book  MATH  Google Scholar 

  19. Mikkelsen, C.J.: Lattice-theoretic and logical aspects of elementary topoi. Aarhus Universitet, Various Publications Series 25 (1976)

    Google Scholar 

  20. Prawitz, D.: Natural Deduction, a Proof-theoretical Study. Uppsala 1965

    Google Scholar 

  21. Scott, D.S.: Existence and description in formal logic, in Bertrand Russell, Philosopher of the Century (Ed. Schoenmann). London: Allen and Unwin 1967, 181–200

    Google Scholar 

  22. Smorynski, C.: Elementary intuitionistic theories. J.S.L. 38, 102–134 (1973)

    MathSciNet  MATH  Google Scholar 

  23. Smorynski, C.: Applications of Kripke models, in Metamathematical investigation of intuitionistic arithmetic and analysis. Lecture Notes in Mathematics, 344. (Ed. Troelstra). Berlin and New York: Springer 1973

    Chapter  Google Scholar 

  24. Smorynski, C.: On axiomatizing fragments. J.S.L., 42, 530–544 (1977)

    MathSciNet  MATH  Google Scholar 

  25. Stenlund, S.: Descriptions in intuitionistic logic, in Proceeding of the Third Scandinavian Logic Symposium (Ed. Kanger). North Holland, 1975, 197–212

    Google Scholar 

  26. Tarski, A.: On the primitive term of logistic, in Logic, Semantics, Metamathematics. Oxford, 1956, 1–23

    Google Scholar 

  27. Troelstra, A.: Aspects of constructive mathematics. In Handbook of Mathematical Logic (ed. Barwise, J.). North-Holland 1977

    Google Scholar 

  28. Troelstra, A.: The interplay between logic and mathematics: intuitionism. Preprint, University of Amsterdam, 1978

    Google Scholar 

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Authors and Affiliations

  1. Merton College, Oxford, England

    Dana Scott

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  1. Dana Scott
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Michael Fourman Christopher Mulvey Dana Scott

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© 1979 Springer-Verlag

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Scott, D. (1979). Identity and existence in intuitionistic logic. In: Fourman, M., Mulvey, C., Scott, D. (eds) Applications of Sheaves. Lecture Notes in Mathematics, vol 753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061839

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  • DOI: https://doi.org/10.1007/BFb0061839

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09564-4

  • Online ISBN: 978-3-540-34849-8

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