Algebra universalis

, Volume 66, Issue 4, pp 405-420

First online:

MacNeille completions of FL-algebras

  • Agata CiabattoniAffiliated withDepartment of Computer Languages, Vienna University of Technology
  • , Nikolaos GalatosAffiliated withDepartment of Mathematics, University of Denver Email author 
  • , Kazushige TeruiAffiliated withResearch Institute for Mathematical Sciences, Kyoto University

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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.

2010 Mathematics Subject Classification

Primary: 03B47 Secondary: 06F05 03G10 08B15

Keywords and phrases

Residuated lattices completions FL-algebras Heyting algebras substructural logics superintuitionistic logics