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Every countably presented formal topology is spatial, classically

  • Silvio Valentini (a1)
Abstract

By using some classical reasoning we show that any countably presented formal topology, namely, a formal topology with a countable axiom set, is spatial.

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[1]Bell, J. and Machover, M.. A course in mathematical logic, North-Holland, Amsterdam. 1977.
[2]Coquand, T.. Sadocco, S., Sambin, G., and Smith, J., Formal topologies on the set of first-order formulae, this Journal, vol. 65 (2000), no. 3, pp. 11831192.
[3]Coquand, T.. Sambin, G., Smith, J., and Valentini, S.. Inductively generated formal topologies, Annals of Pure and Applied Logic, vol. 124 (2003). no. 1–3, pp. 71106.
[4]Engelking, R., General topology. Polish Scientific Publisher, Warszawa, 1977.
[5]Johnston, P. T., Stone spaces, Cambridge Studies in Advanced Mathematics, vol. 3, Cambridge University Press. 1982.
[6]Maguolo, D. and Valentini, S.. An intuitionistic version of Cantor's theorem, Mathematical Logic Quarterly, vol. 42 (1996), pp. 446448.
[7]Maietti, M. E. and Valentini, S.. A structural investigation on formal topology: coreflection of formal covers and exponentiability, this Journal, vol. 69 (2004), no. 4, pp. 9671005.
[8]Martin-Löf, P., Note of constructive mathematics, Almqvist & Wiksell, Stockholm, 1970.
[9]Martin-Löf, P.. Intuitionistic type theory, notes by G. Sambin of a series of lectures given in Padua, Bibliopolis, Naples, 1984.
[10]Sambin, G.. Some points informal topology, Theoretical Computer Science, vol. 305 (2003), no. 1–3, pp. 347408.
[11]Valentini, S., The problem of the formalization of constructive topology, Archive for Mathematical Logic, vol. 44 (2005), pp. 115129.
[12]Valentini, S., Towards a complete formalization of constructive topology, to appear.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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