Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-14T20:19:29.186Z Has data issue: false hasContentIssue false
  • English
  • Français

Every countably presented formal topology is spatial, classically

Published online by Cambridge University Press:  12 March 2014

Silvio Valentini
Silvio Valentini*
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via G. Belzoni N.7, 1-35131 Padova, Italy. E-mail: silvio@math.unipd.it
Get accessRights & Permissions [Opens in a new window]

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.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 2 , June 2006, pp. 491 - 500
Copyright
Copyright © Association for Symbolic Logic 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Bell, J. and Machover, M.. A course in mathematical logic, North-Holland, Amsterdam. 1977.Google Scholar
[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. 1183–1192.Google Scholar
[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. 71–106.CrossRefGoogle Scholar
[4]Engelking, R., General topology. Polish Scientific Publisher, Warszawa, 1977.Google Scholar
[5]Johnston, P. T., Stone spaces, Cambridge Studies in Advanced Mathematics, vol. 3, Cambridge University Press. 1982.Google Scholar
[6]Maguolo, D. and Valentini, S.. An intuitionistic version of Cantor's theorem, Mathematical Logic Quarterly, vol. 42 (1996), pp. 446–448.CrossRefGoogle Scholar
[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. 967–1005.Google Scholar
[8]Martin-Löf, P., Note of constructive mathematics, Almqvist & Wiksell, Stockholm, 1970.Google Scholar
[9]Martin-Löf, P.. Intuitionistic type theory, notes by G. Sambin of a series of lectures given in Padua, Bibliopolis, Naples, 1984.Google Scholar
[10]Sambin, G.. Some points informal topology, Theoretical Computer Science, vol. 305 (2003), no. 1–3, pp. 347–408.CrossRefGoogle Scholar
[11]Valentini, S., The problem of the formalization of constructive topology, Archive for Mathematical Logic, vol. 44 (2005), pp. 115–129.CrossRefGoogle Scholar
[12]Valentini, S., Towards a complete formalization of constructive topology, to appear.Google Scholar