Distributive lattices with a dual homomorphic operation. II

Studia Logica 40 (4):391 - 404 (1981)
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 with respect to which the successor function is decreasing is given.
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DOI 10.1007/BF00401657
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References found in this work BETA
Helena Rasiowa (1974). An Algebraic Approach to Non-Classical Logics. Warszawa, Pwn - Polish Scientific Publishers.
Raymond Balbes & Philip Dwinger (1977). Distributive Lattices. Journal of Symbolic Logic 42 (4):587-588.

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