منابع مشابه
On 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 کاملOn finitely generated Heyting algebras
We study finitely generated Heyting algebras from algebraic and model theoretic points of view. We prove amon others that finitely generated free Heyting algebras embed in their profinite completions, which are projective limits of finitely generated free Heyting algebras of finite dimension.
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 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...
متن کاملFinitely Presented Heyting Algebras
In this paper we study the structure of finitely presented Heyting algebras. Using algebraic techniques (as opposed to techniques from proof-theory) we show that every such Heyting algebra is in fact coHeyting, improving on a result of Ghilardi who showed that Heyting algebras free on a finite set of generators are co-Heyting. Along the way we give a new and simple proof of the finite model pro...
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ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2016
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.757.7ec