Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-06-02T21:00:56.759Z Has data issue: false hasContentIssue false
  • English
  • Français

Forcing in intuitionistic systems without power-set1

Published online by Cambridge University Press:  12 March 2014

R.J. Grayson
R.J. Grayson*
Affiliation:
Institut fur Mathematische Logik, Münster, Federal Republic of Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown how to define forcing semantics within metatheories not containing the power-set construction, in particular, how to construct exponents assuming only (a slightly strengthened form of) exponents in the metatheory. Some straightforward applications (consistency and independence results, and derived rules) are obtained for such systems.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 3 , September 1983 , pp. 670 - 682
Copyright
Copyright © Association for Symbolic Logic 1983

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 work is part of the author's Ph.D. Dissertation at The Hebrew University, Jerusalem. He is grateful to his supervisors, Professors A. Levy and S. Shelah.

References

REFERENCES

[1]Aczel, P., Extending the topological interpretation to constructive set theory (manuscript).Google Scholar
[2]Beeson, M., Principles of continuous choice, Annals of Mathematical Logic, vol. 12 (1977), pp. 249–322.CrossRefGoogle Scholar
[3]Beeson, M., Continuity in intuitionistic set theories, Logic Colloquium '78, Mons, North-Holland, Amsterdam, 1980.Google Scholar
[4]Fourman, M., and Grayson, R.J., Formal spaces, to appear in Proceedings of the Brouwer Meeting, 1981, North-Holland, Amsterdam.Google Scholar
[5]Fourman, M. and Hyland, J. M. E., Sheaf models for analysis, Applications of sheaves, Lecture Notes in Mathematics, vol. 753, Springer, Berlin and New York, 1979, pp. 280–301.CrossRefGoogle Scholar
[6]Fourman, M. and Scott, D.S., The logic of sheaves, Applications of sheaves, Lecture Notes in Mathematics, vol. 753, Springer-Verlag, Berlin and New York, 1979, pp. 302–401.CrossRefGoogle Scholar
[7]Friedman, H., The consistency of classical set theory relative to a set theory with intuitionistic logic, this Journal, vol. 38 (1973), pp. 315–319.Google Scholar
[8]Friedman, H., Set theoretic foundations for constructive analysis, Annals of Mathematics, vol. 105 (1977), pp. 1–28.CrossRefGoogle Scholar
[9]Grayson, R.J., Hey ting-valued models for intuitionistic set theory, Applications of sheaves, Lecture Notes in Mathematics, vol. 753, Springer, Berlin and New York, 1979, pp. 402–414.CrossRefGoogle Scholar
[10]Friedman, H., Heyting-valued semantics, to appear in Logic Colloquium '82, North-Holland, Amsterdam.Google Scholar
[11]Hayashi, S., Notes on bar induction rule, to appear in Proceedings of the Brouwer Meeting, 1981, North-Holland, Amsterdam.Google Scholar
[12]Myhill, J., Constructive set theory, this Journal, vol. 40 (1975), pp. 347–382.Google Scholar
[13]Powell, W., Extending Godel's negative translation to ZF, this Journal, vol. 40, no. 2 (1975), pp. 221–229.Google Scholar
[14]Scott, D. S., Identity and existence in intuitionistic logic, Applications of sheaves, Lecture Notes in Mathematics, vol. 753, Springer, Berlin and New York, 1979, pp. 660–696.CrossRefGoogle Scholar
[15]van Dalen, D., An interpretation of intuitionistic analysis, Annals of Mathematical Logic, vol. 13 (1978), pp. 1–43.CrossRefGoogle Scholar