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Finitely generated free Heyting algebras: the well-founded initial segment

Published online by Cambridge University Press:  12 March 2014

R. Elageili  and
J. K. Truss
R. Elageili
Affiliation:
Department of Mathematics, University of Garyounis ‘Benghazi’, Benghazi, Libya, E-mail: [email protected]
J. K. Truss
Affiliation:
Department of Mathematics, University of Garyounis ‘Benghazi’, Benghazi, Libya, E-mail: [email protected]
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Abstract

In this paper we describe the well-founded initial segment of the free Heyting algebra α on finitely many, α, generators. We give a complete classification of initial sublattices of 2 isomorphic to 1 (called ‘low ladders’), and prove that for 2 ≤ α < ω, the height of the well-founded initial segment of α is ω2.

Keywords

free Heyting algebrawell-foundedlow ladder
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 4 , December 2012 , pp. 1291 - 1307
Copyright
Copyright © Association for Symbolic Logic 2012

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References

REFERENCES

[1]Bellissima, F., Finitely generated free Heyting algebras, this Journal, vol. 51 (1986), pp. 152–165.Google Scholar
[2]Darnière, L. and Junker, M., On Belissima's construction of the finitely generated free Heyting algebras and beyond. Archive for Mathematical Logic, vol. 49 (2010), pp. 743–771.CrossRefGoogle Scholar
[3]Elageili, R., Free Heyting algebras, Ph.D. thesis, University of Leeds, 2011.Google Scholar
[4]Grigolia, R., Free and projective Heyting and monadic Heyting algebras, Non-classical logics and their applications to fuzzy subsets (Höhle, U. and Klement, E. P., editors), Kluwer, 1995, pp. 33–52.CrossRefGoogle Scholar
[5]Johnstone, P. T., Stone spaces, Cambridge University Press, 1982.Google Scholar
[6]Kleene, S. C, Introduction to metamathematics, North-Holland, 1964.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]Riger, L., Zametki o t. naz. svobodnyh algebrah c zamykaniami, Czechoslovak Mathematical Journal, vol. 7 (1957), no. 82, pp. 16–20.Google Scholar
[9]Troelstra, A. S. and van Dalen, D., Constructivism in mathematics, North-Holland, 1988.Google Scholar
[10]Urquhart, A., Free Heyting algebras, Algebra Universalis, vol. 3 (1973), pp. 94–97.CrossRefGoogle Scholar