Abstract
We give a representation of finitely generated free interior algebras and of the Heyting algebras of their open elements. By means of the representation we give a new and strengthened version of some earlier theorems of McKinsey-Tarski and Blok, etc. regarding such algebras.
Similar content being viewed by others
References
F.Bellissima,Atoms in modal algebras, to appear in Zeitschrift für Mathematische Logic
W. J.Blok,The free closure algebra on finitely many generators, Indagationes Mathematicae, 1977, pp 362–379.
W. J.Blok,The lattice of modal logics: an algebraic investigation, Journal of Symbolic Logic, 1980, pp 221–236.
W. J. Blok andPh. Dwinger,Equational classes of closure algebras I, Indagationes Mathematicae,37, pp 189–198, 1975.
S.Burris and H. P.Sankappanavar,A course in Universal Algebra, Springer-Verlag, 1981.
J. C. C. McKinsey andA. Tarski,The algebra of topology, Annals of Mathematics.45, pp 141–191, 1944.
J. C. C. McKinsey andA. Tarski,On closed elements in closure algebras, Annals of Mathematics,47, pp. 122–162, 1946.
M. Mirolli,On the axiomatization of finite frames of the modal system GL, Bollettino U.M.I., 17B, pp 1075–1085, 1980.
H.Rasiowa and R.Sikorski,The mathematics of Metamathematics, Warsawa, 1963.
K.Segerberg,An essay in Classical Modal Logic, Uppsala, 1971.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bellissima, F. An effective representation for finitely generated free interior algebras. Algebra Universalis 20, 302–317 (1985). https://doi.org/10.1007/BF01195140
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01195140