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Topological Proofs of Some Rasiowa-Sikorski Lemmas

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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Correspondence to Robert Goldblatt.

Additional information

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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Keywords

  • Rasiowa-Sikorski Lemma
  • Baire category theorem
  • Priestley topology
  • compact
  • dense
  • lattice
  • distributive
  • Heyting algebra
  • prime filter
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  • meet