Set theory relationships

Continuing this post, in the referenced Edwards book he discussed 3 different kinds of holarchy: developmental, ecological and governance (132). This might or not refer to different kinds of set theory. E.g.: "In true governance holarchies, more encompassing levels do not determine what the less encompassing levels will do in isolation from the organising agency of those junior levels. Higher holarchical levels do not cause lower levels to behave or think. The exchange is always a two-way process. Hence, in a balanced governance holarchy, constituent holons are best seen as leader-followers" (133).

Note the diagrams of the 3 types (figure 7.1). The governance holarchical levels are not subsumed within the higher levels, indicating a different set relationship.

Which of course reminds me of Bryant's discussion of intension and extension relationships in Badiou's set theory. In the former the elements of the set are ordered in a particular way, whereas in the latter the elements can be related in multiple ways. I.e., elements in the latter are not defined by their relations whereas they are in the former. This seems to be the difference between the internal organizational structure of an individual holon and its relationships with other, external holons, similar to Edwards' different types.