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We show that splitting of elements of an independent family of infinite regular size will produce a full size independent set.
We characterize ideals of ortholattices which are congruence kernels. We show that every congruence class determines a kernel.
Let be an MS-algebra with congruence permutable skeleton. We prove that solving a system of congruences in can be reduced to solving the restriction of the system to the skeleton of , plus solving the restrictions of the system to the intervals
Let denote the variety of lattices generated by convex sublattices of lattices in . For any proper variety , the variety is proper. There are uncountably many varieties with .
0. Introduction. Besides being of intrinsic interest, cylindric (semi-) lattices arise naturally from the study of dependencies in relational databases; the polynomials on a cylindric semilattice are closely related to the queries obtainable from project-join mappings on a relational database (cf. [D] for references). This note is intended to initiate the study of these structures, and only a few, rather basic results will be given. Some problems at the end will hopefully stimulate further research....
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