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Profinite Heyting Algebras

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Abstract

For a Heyting algebra A, we show that the following conditions are equivalent: (i) A is profinite; (ii) A is finitely approximable, complete, and completely join-prime generated; (iii) A is isomorphic to the Heyting algebra Up(X) of upsets of an image-finite poset X. We also show that A is isomorphic to its profinite completion iff A is finitely approximable, complete, and the kernel of every finite homomorphic image of A is a principal filter of A.

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003-8001, USA

    G. Bezhanishvili

  2. Department of Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, UK

    N. Bezhanishvili

Authors
  1. G. Bezhanishvili
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  2. N. Bezhanishvili
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Correspondence to G. Bezhanishvili.

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Bezhanishvili, G., Bezhanishvili, N. Profinite Heyting Algebras. Order 25, 211–227 (2008). https://doi.org/10.1007/s11083-008-9089-1

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  • DOI: https://doi.org/10.1007/s11083-008-9089-1

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