Abstract
An Ockham lattice is defined to be a distributive lattice with 0 and 1 which is equipped with a dual homomorphic operation. In this paper we prove: (1) The lattice of all equational classes of Ockham lattices is isomorphic to a lattice of easily described first-order theories and is uncountable, (2) every such equational class is generated by its finite members. In the proof of (2) a characterization of orderings of ω with respect to which the successor function is decreasing is given.
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Urquhart, A. Distributive lattices with a dual homomorphic operation. II. Stud Logica 40, 391–404 (1981). https://doi.org/10.1007/BF00401657
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DOI: https://doi.org/10.1007/BF00401657