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

Volume 195 / 2007

Michael Pinsker Fundamenta Mathematicae 195 (2007), 1-10 MSC: Primary 08A40; Secondary 08A05. DOI: 10.4064/fm195-1-1


The clone lattice $\mathop{\rm Cl}(X)$ 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 $\mathop{\rm Cl}(X)$.


  • Michael PinskerInstitut für Diskrete Mathematik und Geometrie
    Technische Universität Wien
    Wiedner Hauptstraße 8-10/104
    A-1040 Wien, Austria

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