Abstract
A general completeness criterion for the finite product ∏ P(k i) of full partial clones P(k i) (composition-closed subsets of partial operations) defined on finite sets E(k i) (|E(k i)|⩾2, i=1,…,n, n⩾2) is considered and a Galois connection between the lattice of subclones of ∏ P(k i) , called partial n-clones, and the lattice of subalgebras of multiple-base invariant relation algebra, with operations of a restricted quantifier free calculus, is established. This is used to obtain the full description of all maximal partial n-clones via multiple-base invariant relations and, thus, to solve the general completeness problem in ∏ P(k i) .
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