منابع مشابه
Profinite 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...
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In this note we provide a topological description of the MacNeille completion of a Heyting algebra similar to the description of the MacNeille completion of a Boolean algebra in terms of regular open sets of its Stone space. We also show that the only varieties of Heyting algebras that are closed under MacNeille completions are the trivial variety, the variety of all Boolean algebras, and the v...
متن کاملTopo-canonical completions of closure algebras and Heyting algebras
We introduce and investigate topo-canonical completions of closure algebras and Heyting algebras. We develop a duality theory that is an alternative to Esakia’s duality, describe duals of topo-canonical completions in terms of the Salbany and Banaschewski compactifications, and characterize topo-canonical varieties of closure algebras and Heyting algebras. Consequently, we show that ideal compl...
متن کاملProfinite 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 کاملFormal Completions and Idempotent Completions of Triangulated Categories of Singularities
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1997
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(97)00012-2