On homogeneous semilattices and their automorphism groups (Q1970932)

A semilattice \((S,\lor)\) is called homogeneous if each isomorphism between two finite subsemilattices of \(S\) extends to an automorphism of \(S\). It is shown that there are just countably many countable homogeneous semilattices. A semilattice \((S,\lor)\) is said to be universal if each countable semilattice embeds into it. It is proved that the automorphism group of the universal homogeneous countable semilattice has a largest proper nontrivial normal subgroup.