منابع مشابه
Profinite Completions and Canonical Extensions of Heyting Algebras
We show that the profinite completions and canonical extensions of bounded distributive lattices and of Boolean algebras coincide. We characterize dual spaces of canonical extensions of bounded distributive lattices and of Heyting algebras in terms of Nachbin order-compactifications. We give the dual description of the profinite completion ̂ H of a Heyting algebra H, and characterize the dual sp...
متن کاملProfinite Heyting Algebras and Profinite Completions of Heyting Algebras
This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to...
متن کاملExpansions of Heyting algebras
It is well-known that congruences on a Heyting algebra are in one-to-one correspondence with filters of the underlying lattice. If an algebra A has a Heyting algebra reduct, it is of natural interest to characterise which filters correspond to congruences on A. Such a characterisation was given by Hasimoto [1]. When the filters can be sufficiently described by a single unary term, many useful p...
متن کاملOn Heyting algebras and dual BCK-algebras
A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...
متن کاملProfinite Heyting Algebras
For a Heyting algebra A, we show that the following conditions are equivalent: (i) A is profinite; (ii) A is finitely approximable, complete, and completely joinprime generated; (iii) A is isomorphic to the Heyting algebra Up(X) of upsets of an image-finite poset X. We also show that A is isomorphic to its profinite completion iff A is finitely approximable, complete, and the kernel of every fi...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1979
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-41-1-1-12