Representation of Steinitz's lattice in lattices of substructures of relational structures

Oksana Bezushchak, Bogdana Oliynyk, Vitaliy Sushchansky


General conditions under which certain relational structure contains a lattice of substructures isomorphic to Steinitz's lattice are formulated. Under some natural restrictions we consider relational structures with the lattice containing a sublattice isomorphic to the lattice of positive integers with respect to divisibility. We apply to this sublattice a construction that could be called ``lattice completion''. This construction can be used for different types of relational structures, in particular for universal algebras, graphs, metric spaces etc. Some examples are considered.


relational structure, lattice, supernatural numbers, Boolean algebra

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