  We give a model of set theory based on multisets in homotopy type theory. The
equality of the model is the identity type. The underlying type of iterative
sets can be formulated in Martin-L\"of type theory, without Higher Inductive
Types (HITs), and is a sub-type of the underlying type of Aczel's 1978 model of
set theory in type theory. The Voevodsky Univalence Axiom and mere set
quotients (a mild kind of HITs) are used to prove the axioms of constructive
set theory for the model. We give an equivalence to the model provided in
Chapter 10 of "Homotopy Type Theory" by the Univalent Foundations Program.

Logic