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3088 varieties: A solution to the Ackermann constant problem1

Published online by Cambridge University Press:  12 March 2014

John K. Slaney
John K. Slaney*
Affiliation:
Department of Philosophy, University of Edinburgh, Edinburgh EH8 9JX, Scotland
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Abstract

It is shown that there are exactly six normal DeMorgan monoids generated by the idntity element alone. The free DeMorgan monoid with no generators but the identity is characterised and shown to have exactly three thousand and eighty-eight elements. This result solves the “Ackermann constant problem” of describing the structure of sentential constants in the logic R.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 50 , Issue 2 , June 1985 , pp. 487 - 501
Copyright
Copyright © Association for Symbolic Logic 1985

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Footnotes

1

This research was supported by an Australian National University Ph.D. Scholarship, by the Doreen Bretherton Studentship, University of Durham, and by a University of Queensland Postdoctoral Fellowship.

References

REFERENCES

[1]Anderson, A. R. and Belnap, N. D., Entailment: the logic of relevance and necessity. Vol. I, Princeton University Press, Princeton, New Jersey, 1975.Google Scholar
[2]Meyer, R. K., Sentential constants in R, Australian National University Logic Group Research Paper no. 2, Canberra, 1979.Google Scholar
[3]Meyer, R. K. and Routley, F. R., Classical relevant logics. I, Studia Logica, vol. 32 (1973), pp. 51–56.CrossRefGoogle Scholar