Universality of the lattice of transformation monoids

by Pinsker and Shelah. [PnSh:983]
Proc AMS, 2013
The set of all transformation monoids on a fixed set of infinite cardinality lambda, equipped with the order of inclusion, forms an algebraic lattice Mon (lambda) with 2^lambda compact elements. We show that this lattice is universal, i.e., every algebraic lattice with at most 2^lambda compact elements is isomorphic to a complete sublattice of Mon (lambda) .

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