I have been reading Michael Potter's Set Theory and its Philosophy. I am confused by the concept of a history, which I understand is somewhat unconventional. The definition given is as follows:
The accumulation of a, $\mathop{\mathrm{acc}}(a)$, is the set {$x | x \text{ is an urelement or } \exists b \in a (x \in b \text{ or } x \subset b)$}.
If $ \forall v \in V: v = \mathop{\mathrm{acc}}(V\cap v))$ then $V$ is a history.
More information can be found on Wikipedia: https://en.wikipedia.org/wiki/Scott%E2%80%93Potter_set_theory
In particular it would seem that not all sets may be elements of a history, as each element of a history must be equal to an accumulation and thus contain all urelements.
I thought I had some understanding of the iterative conception of sets, which in my mind is linked to some variation on Von Neumann's hierarchy. I am having a hard time linking this to Potter's set theory.
Thank you for any insights or pointers!