  A multiset consists of elements, but the notion of a multiset is
distinguished from that of a set by carrying information of how many times each
element occurs in a given multiset. In this work we will investigate the notion
of iterative multisets, where multisets are iteratively built up from other
multisets, in the context Martin-L\"of Type Theory, in the presence of
Voevodsky's Univalence Axiom.
  Aczel 1978 introduced a model of constructive set theory in type theory,
using a W-type quantifying over a universe, and an inductively defined
equivalence relation on it. Our investigation takes this W-type and instead
considers the identity type on it, which can be computed from the Univalence
Axiom. Our thesis is that this gives a model of multisets. In order to
demonstrate this, we adapt axioms of constructive set theory to multisets, and
show that they hold for our model.
