An effective representation for finitely generated free interior algebras
Copyright policy )An effective representation for finitely generated free interior algebras
An interior algebra (IA) is in fact a closure algebra in which one works with the interior operator \(I=\rceil C\rceil\) instead of the closure operator C. An I-model is the algebraic version of the concept of Kripke model for S4. The author obtains a representation of every finitely generated free IA as an IA of subsets of the set-theoretical union of certain I-models. This yields a representation of the Heyting algebra of all open elements of the free IA as well as certain strengthened versions of several results of \textit{J. C. C. McKinsey} and \textit{A. Tarski} [Ann. Math., II. Ser. 45, 141-191 (1944; Zbl 0060.062); ibid. 47, 122-162 (1946; Zbl 0060.062)] and \textit{W. J. Block} [Indagationes Math. 39, 362-379 (1977; Zbl 0412.03041)].
- University of Siena Italy
closure algebra, Free algebra, representation, Heyting algebra, I-model, Galois correspondences, closure operators (in relation to ordered sets), Representation theory of lattices, 510, Other algebras related to logic, Free lattices, projective lattices, word problems, finitely generated free interior algebras, Heyting algebras (lattice-theoretic aspects), Kripke model
closure algebra, Free algebra, representation, Heyting algebra, I-model, Galois correspondences, closure operators (in relation to ordered sets), Representation theory of lattices, 510, Other algebras related to logic, Free lattices, projective lattices, word problems, finitely generated free interior algebras, Heyting algebras (lattice-theoretic aspects), Kripke model
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