A Homogenizable Fishy Poorset,

Work of Peter Neumannʹs on coprime suborbits of transitive permutation groups led him to consider a class of structures which he called “fishy poorsets.” He asked whether there is a fishy poorset whose automorphism group is transitive on particular classes of triples. By enriching the language of partial orders we “homogenize” the class. The automorphism group of the resulting “homogenized” structure then has the transitivity properties required to solve Neumannʹs problem.