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A Duality for Involutive Bisemilattices

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Abstract

We establish a duality between the category of involutive bisemilattices and the category of semilattice inverse systems of Stone spaces, using Stone duality from one side and the representation of involutive bisemilattices as Płonka sum of Boolean algebras, from the other. Furthermore, we show that the dual space of an involutive bisemilattice can be viewed as a GR space with involution, a generalization of the spaces introduced by Gierz and Romanowska equipped with an involution as additional operation.

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Authors and Affiliations

  1. Università Politecnica delle Marche, Ancona, Italy

    Stefano Bonzio

  2. Università di Cagliari, Cagliari, Italy

    Andrea Loi & Luisa Peruzzi

Authors
  1. Stefano Bonzio
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  2. Andrea Loi
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  3. Luisa Peruzzi
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Correspondence to Stefano Bonzio.

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Presented by Constantine Tsinakis

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Bonzio, S., Loi, A. & Peruzzi, L. A Duality for Involutive Bisemilattices. Stud Logica 107, 423–444 (2019). https://doi.org/10.1007/s11225-018-9801-0

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