Abstract
Some sets of taxonomic models can be structured as meet-semilattices having the properties that (i) every principal ideal is a distributive lattice and (ii) each finite subset has an upper bound whenever each of its (n−1)-subsets is bounded above, where n≥3 is a fixed number. Every such semilattice is endowed with an n-ary near-unanimity operation. We show that for n≥4 one can define these semilattices solely in terms of this n-ary operation. The resulting algebras are subdirect powers of two-element algebras, and of course, generalize median algebras.
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Communicated by I. Rival
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Bandelt, HJ., Meletiou, G.C. An algebraic setting for near-unanimity consensus. Order 7, 169–178 (1990). https://doi.org/10.1007/BF00383764
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DOI: https://doi.org/10.1007/BF00383764