Clans, parent sets, litters, atoms, and allowable permutations

Introductory remarks: In this note I am trying to separate out another theme in my NF consistency proof, namely the basic maneuver behind the FM construction. The advantage of this approach is that it makes it clear that the properties of the system of atoms, clans and litters constructed depend to very different degrees on the insane definition of the parent sets, which in this approach is introduced rather late. There is however no circularity in this presentation: an abstract definition of systems of clans and parent sets is given, then more and more intended properties of parent sets are assumed in further arguments until the insane specification is fully revealed. I believe that it is quite clear that the partial specifications given up to that point are all realizable in well-founded ways. Also, it is possible to motivate the insane definition of the parent sets in this document, because one knows enough about the properties of systems of clans and litters at the time it is introduced to be able to see that it will have the desired effect, if it is possible.