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Two variable implicational calculi of prescribed many-one degrees of unsolvability

Published online by Cambridge University Press:  12 March 2014

Charles E. Hughes
Charles E. Hughes*
Affiliation:
University of Tennessee, Knoxville, Tennessee 37916
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Abstract

A constructive proof is given which shows that every nonrecursive r.e. many-one degree is represented by the family of decision problems for partial implicational propositional calculi whose well-formed formulas contain at most two distinct variable symbols.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 41 , Issue 1 , March 1976 , pp. 39 - 44
Copyright
Copyright © Association for Symbolic Logic 1976

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References

REFERENCES

[1] Gladstone, M. D., On the number of variables in the axioms, Notre Dame Journal of Formal Logic, vol. 11 (1970), pp. 1–15.CrossRefGoogle Scholar
[2] Hughes, C. E., Two variable implicational calculi, this Journal, vol. 39 (1974), p. 403. Abstract.Google Scholar
[3] Hughes, C. E. and Singletary, W. E., Triadic partial implicational propositional calculi, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 21 (1975), pp. 21–28.CrossRefGoogle Scholar
[4] Overbeek, Ross, The representation of many-one degrees by decision problems of Turing machines, Proceedings of the London Mathematical Society (3), vol. 26 (1973), pp. 167–183.CrossRefGoogle Scholar
[5] Singletary, W. E., Recursive unsolvability of a complex of problems proposed by Post, Journal of the Mathematical Society of Japan, vol. 14 (1967), pp. 25–58.Google Scholar
[6] Wajsberg, M., Axiomatization of the three-valued propositional logic, Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie Classe II, vol. 24 (1931).Google Scholar
[7] Yntema, M. K., A detailed argument for the Post-Linial theorems, Notre Dame Journal of Formal Logic, vol. 5 (1964), pp. 37–51.CrossRefGoogle Scholar