Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-14T17:38:51.940Z Has data issue: false hasContentIssue false
  • English
  • Français

The implicational fragment of Dummett's LC

Published online by Cambridge University Press:  12 March 2014

R. A. Bull
R. A. Bull*
Affiliation:
Manchester University
Get access Rights & Permissions [Opens in a new window]

Extract

It has been shown in Dummett [1] that the system LC given by Heyting's Calculus plus the additional axiom ACpqCqp is complete with respect to the model having as truth values the integers 0, 1,2, … and ω, 0 being the designated value, with

In this system CCCpqrCCCqprr is equivalent to ACpqCqp, and the purpose of this paper is to show that the implicational fragment of Heyting's Calculus plus the additional axiom CCCpqrCCCqprr yields the implicational fragment of LC.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 27 , Issue 2 , June 1962 , pp. 189 - 194
Copyright
Copyright © Association for Symbolic Logic 1962

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]Dummett, Michael, A prepositional calculus with denumerable matrix, this Journal, vol. 24 (1959) pp. 96–107.Google Scholar
[2]Prior, A. N., Logicians at play; or Syll, Simp and Hilbert, Australasian Journal of Philosophy, vol. 34 (1956), pp. 182–192.CrossRefGoogle Scholar