Lattices of suborders (Q1307163)

The lattices of suborders of partial orders are studied. In particular, the author gives a description for upper semidistributive lattices of suborders, characterizes such lattices for finite orderings (as those satisfying each of the following three conditions: the Freese-Nation minimality condition, the Jónsson property, the McKenzie property), obtains a sufficient condition for a lattice satisfying the Freese-Nation minimality condition to be isomorphic to a sublattice of suborderings (from the proof of this result, the author obtains a new proof of the embedding theorem of \textit{B. Sivák} [Math. Slovaca 28, No. 2, 203-215 (1978; Zbl 0395.06002)]), and describes lattices of suborders that possess the complete Jónsson property introduced by the author.