, Volume 66, Issue 4, pp 405-420

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.

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