منابع مشابه
Injective and Projective Heyting Algebras^) by Raymond Balbes and Alfred Horn
The determination of the injective and projective members of a category is usually a challenging problem and adds to knowledge of the category. In this paper we consider these questions for the category of Heyting algebras. There has been a lack of uniformity in terminology in recent years. In [6] Heyting algebras are referred to as pseudo-Boolean algebras, and in [1] they are called Brouwerian...
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 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: Transactions of the American Mathematical Society
سال: 1970
ISSN: 0002-9947
DOI: 10.2307/1995388