Partially Homogeneous Partially Ordered Sets

Abstract We construct continuum many nonisomorphic ℵ 0 -categorical posets which are 3- and not 4-homogeneous. Variants of our construction yield 2- and not 3-homogeneous posets, and yield as many non-ℵ 0 -categorical posets with the same degree of homogeneity. These examples answer questions of Droste and Macpherson.