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Finitely generated free Heyting algebras

Published online by Cambridge University Press:  12 March 2014

Fabio Bellissima
Fabio Bellissima*
Affiliation:
Dipartimento di Matematica, Via Del Capitano 15, 53100 Siena, Italy
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Abstract

The aim of this paper is to give, using the Kripke semantics for intuitionism, a representation of finitely generated free Heyting algebras. By means of the representation we determine in a constructive way some set of “special elements” of such algebras. Furthermore, we show that many algebraic properties which are satisfied by the free algebra on one generator are not satisfied by free algebras on more than one generator.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 51 , Issue 1 , March 1986 , pp. 152 - 165
Copyright
Copyright © Association for Symbolic Logic 1986

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References

REFERENCES

[1]Balbes, R. and Dwinger, P., Distributive lattices, University of Missouri Press, Columbia, Missouri, 1974.Google Scholar
[2]Bellissima, F., Atoms in modal algebras, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 30 (1984), pp. 303–312.CrossRefGoogle Scholar
[3]Bellissima, F., An effective representation for finitely generated free interior algebras, Algebra Universalis (to appear).Google Scholar
[4]Burris, S. and Sankappanavar, H. P., A course in universal algebra, Springer-Verlag, New York, 1981.CrossRefGoogle Scholar
[5]Kripke, S., Semantical analysis of intuitionistic logic. I, Formal systems and recursive functions (proceedings of the eighth logic colloquium, Oxford, 1963; Crossley, J N. and Dummett, M.A.E., editors), North-Holland, Amsterdam, 1965, pp. 92–130.Google Scholar
[6]McKinsey, J. C. C. and Tarski, A., On closed elements in closure algebras, Annals of mathematics, set. 2, vol. 47 (1946), pp. 122–162.Google Scholar
[7]Nishimura, I., On formulas in one variable in intuitionistic propositional calculus, this Journal, vol. 25 (1960), pp. 327–331.Google Scholar
[8]Rasiowa, H., An algebraic approach to non-classical logics, North-Holland, Amsterdam, 1974.Google Scholar
[9]Rigér, L. [Rieger], Zamétka o t. naz. svobodnyh algébrah c zamykaniámi, Czechoslovak Mathematical Journal, vol. 7(82) (1957), pp. 16–20.Google Scholar
[10]Šehtman, V. B., Rieger-Nishimura lattices, Soviet Mathematics—Doklady, vol. 19 (1978) pp. 1014–1018.Google Scholar
[11]Urquhart, A., Free Heyting algebras, Algebra Universalis, vol. 3 (1973), pp. 94–97.Google Scholar