[seanhunter]

> Yes -- in set theory sets can contain themselves

Hrbacek and Jech would like a word. It is very much not the case that in standard axiomatic set theory sets can contain themselves, precisely because this leads to things like Russell’s paradox. Sets containing themselves is generally prevented by the axiom of regularity. (Every non-empty set S contains an element wihch is disjoint from S) https://en.wikipedia.org/wiki/Axiom_of_regularity

> types are not sets and sets are not types

This is also not true. All types can be expressed as sets but not all sets are types in the standard definitions.