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MacNeille completions of FL-algebras

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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.

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Correspondence to Nikolaos Galatos.

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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).

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