Annals of Pure and Applied Logic 171 (10):102842 (2020)

We present a systematic study of join-extensions and join-completions of partially ordered algebras, which naturally leads to a refined and simplified treatment of fundamental results and constructions in the theory of ordered structures ranging from properties of the Dedekind–MacNeille completion to the proof of the finite embeddability property for a number of varieties of lattice-ordered algebras.
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DOI 10.1016/j.apal.2020.102842
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