MacNeille completions of FL-algebras
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- 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.