The Cuntz semigroup of unital commutative AI-algebras

We provide an abstract characterization for the Cuntz semigroup of unital commutative AI-algebras, as well as a characterization for abstract Cuntz semigroups of the form $\text{Lsc}(X,\bar{\mathbb{N}})$ for some $T_1$-space $X$. In our investigations, we also uncover new properties that the Cuntz semigroup of all AI-algebras satisfies.