A Petri net model is referred to as Boolean if the only possible markings are sets, ie, places are marked or not without further quantification; moreover, also the enabling conditions and firing rule are based on this principle of set-based token arithmetic. Elementary Net systems are an example of a class of Boolean nets, and so are the recently introduced set-nets. In our investigation of the synthesis problem for set-nets, it would be useful to know how this new net model can be fitted into the general theory of net synthesis based on the generic concept of τ-nets. Here, we demonstrate how set-nets and the idea of Boolean operations on tokens provide an opportunity to classify a wide variety of Boolean nets that are amenable to region-based net synthesis.