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  • Online publication date: March 2017

Predicativity problems in point-free topology

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Logic Colloquium '03
  • Online ISBN: 9781316755785
  • Book DOI: https://doi.org/10.1017/9781316755785
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P., Aczel [1986], The type-theoretic interpretation of constructive set theory: inductive definitions, Logic, methodology and philosophy of science VII (R.B., Marcus et al., editors), North- Holland, Amsterdam.
P., Aczel [2002], Aspects of general topology in constructive set theory, to appear in Annals of Pure and Applied Logic.
M.A., Armstrong [1983], Basic topology, Springer.
E., Bishop [1967], Foundations of constructive analysis, McGraw-Hill, New York.
E., Bishop and D., Bridges [1985], Constructive analysis, Springer, Berlin.
F., Borceux [1994], Handbook of categorical algebra, vol. 3, Cambridge University Press.
T., Coquand [1995], A constructive topological proof of van der Waerden's theorem, Journal of Pure and Applied Algebra, vol. 105, no. 3, pp. 251–259.
T., Coquand, G., Sambin, J., Smith, and S., Valentini [2003], Inductively generated formal topologies, Annals of Pure and Applied Logic, vol. 124, pp. 71–106.
G., Curi [2002], Compact Hausdorff spaces are data types, Preliminary version, July 30, 2002. To appear in Annals of Pure and Applied Logic.
G., Curi [2003], Exact approximations to Stone-Cech compactification, Manuscript.
P., Dybjer [2000], A general formulation of simultaneous inductive-recursive definitions in type theory, The Journal of Symbolic Logic, vol. 65, pp. 525–549.
P., Dybjer and A., Setzer [2003], Induction-recursion and initial algebras, Annals of Pure and Applied Logic, vol. 124, pp. 1–47.
N., Gambino [2002], Sheaf interpretations for generalised predicative intuitionistic systems, Ph.D. thesis, Manchester University,Manchester.
P.T., Johnstone [1982], Stone spaces, Cambridge University Press.
P., Martin-Löf [1984], Intuitionistic type theory, Notes by G. Sambin of a series of lectures given in Padua, June 1980, Studies in Proof Theory 1, Bibliopolis, Naples.
P., Martin-Löf [1998], An intuitionistic theory of types, Twenty-five years of constructive type theory (G., Sambin and J.M., Smith, editors), Oxford, (First published as a preprint from the Department of Mathematics, University of Stockholm, 1972.).
I., Moerdijk and E., Palmgren [2002], Type theories, toposes and constructive set theory: predicative aspects of AST, Annals of Pure and Applied Logic, vol. 114, pp. 155–201.
S., Negri and D., Soravia [1999], The continuum as a formal space, Archive for Mathematical Logic, vol. 38, no. 7, pp. 423–447.
E., Palmgren [1998], On universes in type theory, Twenty-five years of constructive type theory (G., Sambin and J.M., Smith, editors), Oxford University Press.
E., Palmgren [2002a], Maximal and partial points in formal spaces, Report 2002:23, Uppsala University, Department of Mathematics, URL: www.math.uu.se. To appear in Annals of Pure and Applied Logic.
E., Palmgren [2002b], Regular universes and formal spaces, Report 2002:42, Uppsala University, Department of Mathematics, URL: www.math.uu.se. To appear in Annals of Pure and Applied Logic.
E., Palmgren [2003], Continuity on the real line and in formal spaces, Report 2003:32, Uppsala University, Department ofMathematics, URL: www.math.uu.se.
G., Sambin [1987], Intuitionistic formal spaces — a first communication, Mathematical logic and its applications (D., Skordev, editor), Plenum Press, pp. 187–204.
G., Sambin [2003], Some points in formal topology, Theoretical Computer Science, vol. 305, pp. 347–408.
I., Sigstam [1995], Formal spaces and their effective presentations, Archive for Mathematical Logic, vol. 34, pp. 211–246.
I., Sigstam and V., Stoltenberg-Hansen [1997], Representability of locally compact spaces by domains and formal spaces, Theoretical Computer Science, vol. 179, pp. 319–331.
S.G., Simpson [1999], Subsystems of second order arithmetic, Springer.
H., Weyl [1918], Das Kontinuum: Kritische Untersuchungen über die Grundlagen der Analysis, Veit, Leipzig.