Topological Proofs of Some Rasiowa-Sikorski Lemmas

Studia Logica 100 (1-2):175-191 (2012)
We give topological proofs of Görnemann’s adaptation to Heyting algebras of the Rasiowa-Sikorski Lemma for Boolean algebras; and of the Rauszer-Sabalski generalisation of it to distributive lattices. The arguments use the Priestley topology on the set of prime filters, and the Baire category theorem. This is preceded by a discussion of criteria for compactness of various spaces of subsets of a lattice, including spaces of filters, prime filters etc
Keywords Rasiowa-Sikorski Lemma  Baire category theorem  Priestley topology  compact  dense  lattice  distributive  Heyting algebra  prime filter  join  meet
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DOI 10.1007/s11225-012-9374-2
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