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Algebraic lattices are complete sublattices of the clone lattice over an infinite set

Michael Pinsker — 2007

Fundamenta Mathematicae

The clone lattice Cl(X) over an infinite set X is a complete algebraic lattice with $2^{| X |}$ compact elements. We show that every algebraic lattice with at most $2^{| X |}$ compact elements is a complete sublattice of Cl(X).

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