Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T06:15:45.410Z Has data issue: false hasContentIssue false
  • English
  • Français

Reductibilities in intuitionistic topology1

Published online by Cambridge University Press:  12 March 2014

Dirk Van Dalen
Dirk Van Dalen*
Affiliation:
Massachusetts Institute of Technology and Rijksuniversiteit, Utrecht
Get access Rights & Permissions [Opens in a new window]

Extract

In intuitionistic mathematics one distinguishes between sets with a constructive character and sets in a more general sense. The first kind consists of spreads and the latter of species. The definition of a spread utilizes so-called choice sequences (in [5] infinitely proceeding sequence or ips), i.e., sequences of well-determined mathematical objects which are chosen more or less freely. One can restrict the choices by some law, which, however, need not be predetermined (changing one's mind is allowed).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 3 , 10 October 1968 , pp. 412 - 417
Copyright
Copyright © Association for Symbolic Logic 1968

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.)

Footnotes

1

This research was supported in part by National Science Foundation grant GP-4361.

Part of the material has for the first time been presented at a seminar at the Massachusetts Institute of Technology.

References

[1]Brouwer, L. E. J., Zur Begründung der intuitionistischen Mathematik. I, Mathematische Annalen, vol. 93 (1924), pp. 244–258.CrossRefGoogle Scholar
[2]Brouwer, L. E. J., Intuitionistische Einführung des Dimensionsbegriffes, Proceedings Akad. Amsterdam, vol. 29 (1926), pp. 855–864.Google Scholar
[3]Brouwer, L. E. J., Points and spaces, Canadian journal of mathematics, vol. 6 (1954), pp. 1–17.CrossRefGoogle Scholar
[4]Freudenthal, H., Zum intuitionistischen Raumbegriff, Compositlo mathematica, vol. 4 (1936), pp. 82–111.Google Scholar
[5]Heyting, A., Intuitionism. An introduction, North-Holland, Amsterdam, 1956.Google Scholar
[6]Van Dalen, D., Seminar on intuitionistic mathematics, Massachusetts Institute of Technology, 1965 (mimeographed).Google Scholar
[7]Van Rootselaar, B., On the mapping of spreads, Indagationes mathematicae, vol. 17 (1955), pp. 557–563.CrossRefGoogle Scholar
[8]Van Rootselaar, B., Generating schemes for fulll mappings, Indagationes mathematicae, vol. 17 (1955), pp. 646–649.CrossRefGoogle Scholar