Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T12:51:45.040Z Has data issue: false hasContentIssue false
  • English
  • Français

A complete and consistent modal set theory

Published online by Cambridge University Press:  12 March 2014

Frederic B. Fitch
Frederic B. Fitch*
Affiliation:
Yale University
Get access Rights & Permissions [Opens in a new window]

Extract

1.1. The aim of this paper is the construction of a demonstrably consistent system of set theory that (1) contains roughly the same amount of mathematics as the writer's system K′ [3], including a theory of continuous functions of real numbers, and (2) provides a way for expressing in the object language various propositions which, in the case of K′, could be expressed only in the metalanguage, for example, general propositions about all real numbers. It was not originally intended that the desired system should be a modal logic, but the modal character of the system appears to be a natural outgrowth of the way it is constructed. A detailed treatment of the natural, rational, and real numbers is left for a subsequent paper.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 1 , June 1967 , pp. 93 - 103
Copyright
Copyright © Association for Symbolic Logic 1967

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.)

References

[1]Curry, H. B. and Feys, R., Combinatory logic, vol. I. North-Holland Publishing Company, Amsterdam, 1958.Google Scholar
[2]Fitch, F. B., Intuitionistic modal logic with quantifiers, Portugaliae mathematica, vol. 7 (1948), pp. 113–118.Google Scholar
[3]Fitch, F. B., A demonstrably consistent mathematics, this Journal, vol. 15 (1950), pp. 17–24; vol. 16 (1951), pp. 121–124.Google Scholar
[4]Fitch, F. B., The system CΔ of combinatory logic, this Journal, vol. 28 (1963), pp. 87–97.Google Scholar
[5]Fitch, F. B., Natural deduction rules for obligation, American philosophical quarterly, vol. 3 (1966), pp. 27–38.Google Scholar
[6]Fitch, F. B., A theory of logical essences, Forthcoming in The monist.Google Scholar
[7]Hintikka, J., Knowledge and belief, Cornell University Press, Ithaca, N.Y., 1962.Google Scholar
[8]Kripke, S. A., Semantical analysis of modal logic. I, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 9 (1963), pp. 67–96.CrossRefGoogle Scholar
[9]Kripke, S. A., Semantical considerations in modal logic, Acta philosophlca fennica, vol. 16 (1963), pp. 83–94.Google Scholar