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A geometric proof of the completeness of the Łukasiewicz calculus

Published online by Cambridge University Press:  12 March 2014

Giovanni Panti
Giovanni Panti*
Affiliation:
Department of Mathematics, University of Siena, Via Del Capitano 15, 53100 Siena, Italy, E-mail: panti@sivax.unisi.it
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Abstract

We give a self-contained geometric proof of the completeness theorem for the infinite-valued sentential calculus of Łukasiewicz.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 2 , June 1995 , pp. 563 - 578
Copyright
Copyright © Association for Symbolic Logic 1995

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References

REFERENCES

[1] Chang, C. C., Algebraic analysis of many valued logics, Transactions of the American Mathematical Society, vol. 88 (1958), pp. 467–490.CrossRefGoogle Scholar
[2] Chang, C. C., A new proof of the completeness of the Łukasiewicz axioms, Transactions of the American Mathematical Society, vol. 93 (1959), pp. 74–80.Google Scholar
[3] Cignoli, R., Free lattice-ordered abelian groups and varieties of MV algebras, IXth Latin American Symposium on Mathematical Logic, Notas de Matemática, vol. 38, Universidad Nacional del Sur, Bahia Blanca, Argentina, 1994, pp. 113–118.Google Scholar
[4] De Concini, C. and Procesi, C., Complete symmetric varieties, II, Algebraic groups and related topics (Hotta, R., editor), Kinokuniya, Tokyo, and North-Holland, Amsterdam, 1985, pp. 481–513.CrossRefGoogle Scholar
[5] McNaughton, R., A theorem about infinite-valued sentential logic, this Journal, vol. 16 (1951), pp. 1–13.Google Scholar
[6] Mundici, D., Interpretation of AF C*-algebras in Łukasiewicz sentential calculus, Journal of Functional Analysis, vol. 65 (1986), pp. 15–63.CrossRefGoogle Scholar
[7] Mundici, D., A constructive proof of McNaughton's theorem in infinite-valued logic, this Journal, vol. 59 (1994), pp. 596–602.Google Scholar
[8] Mundici, D. and Pasquetto, M., A proof of the completeness of the infinite-valued calculus of Łukasiewicz with one variable, Nonclassical logics and their applications (Höhle, U. and Klement, E. P., editors), Kluwer, Dordrecht, 1994.Google Scholar
[9] Oda, T., Lectures on torus embeddings and applications, Tata Institute of Fundamental Research, Bombay, and Springer, Berlin, 1978.Google Scholar
[10] Oda, T., Convex bodies and algebraic geometry, Springer, Berlin, 1988.Google Scholar
[11] Rose, A. and Rosser, J. B., Fragments of many-valued sentential calculus, Transactions of the American Mathematical Society, vol. 87 (1958), pp. 1–53.CrossRefGoogle Scholar
[12] Rourke, C. P. and Sanderson, B. J., Introduction to piecewise-linear topology, Springer, Berlin, 1972.CrossRefGoogle Scholar
[13] Semadeni, Z., Schauder bases in Banach spaces of continuous functions, Lecture Notes in Mathematics, vol. 918, Springer, Berlin, 1982.CrossRefGoogle Scholar