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Gödel algebras: interactive dualities and their applications

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Abstract

We present a technique for deriving certain new natural dualities for any variety of algebras generated by a finite Heyting chain. The dualities we construct are tailored to admit a transparent translation to the more pictorial Priestley/Esakia duality and back again. This enables us to combine the two approaches and so to capitalise on the virtues of both, in particular the categorical good behaviour of a natural duality: we thereby demonstrate the fullness, or not, of each of our dualities; we obtain new results on amalgamation; and we also provide a simple treatment of coproducts.

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Authors and Affiliations

  1. Dipartimento di Statistica, Informatica, Applicazioni, Università degli Studi di Firenze, 59, Viale Morgani, 50134, Italy

    L. M. Cabrer

  2. Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Oxford, OX2 6GG, United Kingdom

    H. A. Priestley

Authors
  1. L. M. Cabrer
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  2. H. A. Priestley
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Correspondence to H. A. Priestley.

Additional information

Presented by R. Quackenbush.

Dedicated to Brian Davey in celebration of his 65th birthday

The first author was supported by a Marie Curie Intra European Fellowship within the 7th European Community Framework Program (ref. 299401-FP7-PEOPLE-2011-IEF).

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Cabrer, L.M., Priestley, H.A. Gödel algebras: interactive dualities and their applications. Algebra Univers. 74, 87–116 (2015). https://doi.org/10.1007/s00012-015-0339-y

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  • DOI: https://doi.org/10.1007/s00012-015-0339-y

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