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Distributive Lattices with a Dual Homomorphic Operation. II

Alasdair Urquhart
Studia Logica: An International Journal for Symbolic Logic
Vol. 40, No. 4 (1981), pp. 391-404
Published by: Springer
Stable URL: http://www.jstor.org/stable/20000226
Page Count: 14
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Distributive Lattices with a Dual Homomorphic Operation. II
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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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