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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References found in this work BETA
On Closed Elements in Closure Algebras.J. C. C. Mckinsey & Alfred Tarski - 1946 - Journal of Symbolic Logic 11 (3):83-84.
Notes on the Rasiowa-Sikorski Lemma.Cecylia Rauszer & Bogdan Sabalski - 1975 - Studia Logica 34 (3):265 - 268.
A Proof of the Completeness Theorem of Godel.H. Rasiowa & R. Sikorski - 1952 - Journal of Symbolic Logic 17 (1):72-72.

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