Algebra universalis

, Volume 66, Issue 4, pp 405–420

MacNeille completions of FL-algebras

  • Agata Ciabattoni
  • Nikolaos Galatos
  • Kazushige Terui

DOI: 10.1007/s00012-011-0160-1

Cite this article as:
Ciabattoni, A., Galatos, N. & Terui, K. Algebra Univers. (2011) 66: 405. doi:10.1007/s00012-011-0160-1


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: 03B47Secondary: 06F0503G1008B15

Keywords and phrases

Residuated latticescompletionsFL-algebrasHeyting algebrassubstructural logicssuperintuitionistic logics

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Agata Ciabattoni
    • 1
  • Nikolaos Galatos
    • 2
  • Kazushige Terui
    • 3
  1. 1.Department of Computer LanguagesVienna University of TechnologyWienAustria
  2. 2.Department of MathematicsUniversity of DenverDenverUSA
  3. 3.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan