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The truth about some Post numbers

Published online by Cambridge University Press:  12 March 2014

Krister Segerberg
Krister Segerberg*
Affiliation:
Åbo Academy, 20500 Åbo 50, Finland
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Extract

There is a mistake in [6], discovered by Robert V. Kohn: contrary to the claim on p. 714, the set {◊X i : i ≥ 2} is not independent in S3. As a result three problems thought to be settled are open once more, viz., whether the Post numbers of S2, S3, and K4 are denumerable. In [6] it was claimed they are not. Now we shall prove that that claim is indeed correct for S2 and K4 but, surprisingly enough, not for S3.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 41 , Issue 1 , March 1976 , pp. 239 - 244
Copyright
Copyright © Association for Symbolic Logic 1976

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References

REFERENCES

[1] Halldén, Sören, Results concerning the decision problem of Lewis's calculi S3 and S6, this Journal, vol. 14 (1950), pp. 230–236.Google Scholar
[2] Kohn, Robert V., Some Post-complete extensions of S2 and S3, Notre Dame Journal of Formal Logic (to appear).Google Scholar
[3] Makinson, David and Segerberg, Krister, Post completeness and ultrafilters, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 20 (1974), pp. 385–388.CrossRefGoogle Scholar
[4] Segerberg, Krister, An essay in classical modal logic, Philosophical Society and Department of Philosophy, University of Uppsala, Uppsala, no. 13, 1971.Google Scholar
[5] Segerberg, Krister, On Post completeness in modal logic, this Journal, vol. 37 (1972), pp. 781–782. (Abstract.)Google Scholar
[6] Segerberg, Krister, Post completeness in modal logic, this Journal, vol. 37 (1972), pp. 711–715.Google Scholar
[7] Shukla, Anjan, Consistent, independent, and distinct propositions, Notre Dame Journal of Formal Logic, vol. 13 (1972), pp. 399–406.CrossRefGoogle Scholar