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MacNeille completions of FL-algebras

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Abstract

We show that a large number of equations are preserved by Dedekind-MacNeille completions when applied to subdirectly irreducible FL-algebras/residuated lattices. These equations are identified in a systematic way, based on proof-theoretic ideas and techniques in substructural logics. It follows that many varieties of Heyting algebras and FL-algebras admit completions.

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Authors and Affiliations

  1. Department of Computer Languages, Vienna University of Technology, Favoritenstrasse 9-11, 1040, Wien, Austria

    Agata Ciabattoni

  2. Department of Mathematics, University of Denver, 2360 S. Gaylord St., Denver, CO, 80208, USA

    Nikolaos Galatos

  3. Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto, 606-8502, Japan

    Kazushige Terui

Authors
  1. Agata Ciabattoni
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  2. Nikolaos Galatos
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  3. Kazushige Terui
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Corresponding author

Correspondence to Nikolaos Galatos.

Additional information

Presented by J. Raftery.

A. Ciabattoni was supported by FWF-START Y 544-N23; K. Terui was supported by JSPS KAKENHI 21700041.

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Ciabattoni, A., Galatos, N. & Terui, K. MacNeille completions of FL-algebras. Algebra Univers. 66, 405–420 (2011). https://doi.org/10.1007/s00012-011-0160-1

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  • DOI: https://doi.org/10.1007/s00012-011-0160-1

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