Abstract
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.
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In memory of Leo Esakia
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Goldblatt, R. Topological Proofs of Some Rasiowa-Sikorski Lemmas. Stud Logica 100, 175–191 (2012). https://doi.org/10.1007/s11225-012-9374-2
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DOI: https://doi.org/10.1007/s11225-012-9374-2