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Ten modal models

Published online by Cambridge University Press:  12 March 2014

Ivo Thomas
Ivo Thomas*
Affiliation:
University of Notre Dame, Indiana
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Extract

We consider the results of adding to a basic modal system T0 the axioms G1. CLpp; Pn. CLnpLn+1p; Bn. CpLnMp, where n ≧ 11, in all combinations. The method of Meredith's [7] will be extended to get models of these systems in lower predicate calculus (LPC) with a constant binary relation, U. Most of the results were already obtained in [1]–[6], though systems as in (i) and (ii) below were not investigated, except that S40 in (ii) was mentioned in [1]. However some repetition may be excused in view of the simplicity with which the results are obtained by the present method.

Type
Articles
Information
The Journal of Symbolic Logic , Volume 29 , Issue 3 , September 1964 , pp. 125 - 128
Copyright
Copyright © Association for Symbolic Logic 1964

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References

[1]Sobociński, B., A contribution to the axiomatization of Lewis' S5. Notre Dame Journal of Formal Logic, III (1962), 51–60.Google Scholar
[2]Sobociński, B., On the generalized Brouwerian axioms. Notre Dame Journal of Formal Logic, III (1962), 123–128.Google Scholar
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[6]Thomas, Ivo, Modal Systems in the neighbourhood of T. Notre Dame Journal of Formal Logic, forthcoming.Google Scholar
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