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First steps in synthetic domain theory

Part I

Part of the Lecture Notes in Mathematics book series (LNM,volume 1488)

Keywords

  • Domain Theory
  • Internal Logic
  • Bottom Element
  • Inclusion Order
  • Initial Algebra

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References

  1. P. Freyd, P. Mulry, G. Rosolini and D. S. Scott. ‘Extensional PERs.’ In: Proceedings of the 5th Annual Symposium on Logic in Computer Science (1990) 346–354.

    Google Scholar 

  2. J. M. E. Hyland. ‘A small complete category.’ Annals of Pure and Applied Logic, 40 (1988) 135–165.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. J. M. E. Hyland, E. P. Robinson and G. Rosolini. ‘The discrete objects in the effective topos.’ Proc. Lond. Math. Soc. (3) 60 (1990) 1–36.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. P. T. Johnstone. ‘On a topological topos.’ Proc. Lond. Math. Soc. (3) 38 (1979) 237–271.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. P. T. Johnstone. 'scott is not always sober.’ In: Lecture Notes in Mathematics 871, Springer-Verlag, 1981, 282–283.

    Google Scholar 

  6. P. Mulry. ‘Generalized Banach-Mazur functionals in the topos of recursive sets.’ J. Pure and Appl. Alg. 26 (1981) 71–83.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. W. Phoa. ‘Effective domains and intrinsic structure.’ In: Proceedings of the 5th Annual Symposium on Logic in Computer Science, (1990) 366–377.

    Google Scholar 

  8. W. Phoa. Domain Theory in Realizability Toposes. Ph. D. Thesis, Cambridge, 1990.

    Google Scholar 

  9. E. P. Robinson. ‘How complete is PER?’ In: Proceedings of the 4th Annual Symposium on Logic in Computer Science, (1989).

    Google Scholar 

  10. G. Rosolini. Continuity and effectiveness in topoi. D.Phil. Thesis, Oxford, 1986.

    Google Scholar 

  11. G. Rosolini. ‘Categories and effective computations.’ In: Lecture Notes in Computer Science 283, Springer-Verlag, 1987, 1–11.

    Google Scholar 

  12. T. Streicher. ‘Independence results for calculi of dependent types.’ In: Lecture Notes in Computer Science 389, Springer-Verlag, 1989, 141–154.

    Google Scholar 

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© 1991 Springer-Verlag

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Hyland, J.M.E. (1991). First steps in synthetic domain theory. In: Carboni, A., Pedicchio, M.C., Rosolini, G. (eds) Category Theory. Lecture Notes in Mathematics, vol 1488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084217

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  • DOI: https://doi.org/10.1007/BFb0084217

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  • Print ISBN: 978-3-540-54706-8

  • Online ISBN: 978-3-540-46435-8

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