Isomorphism theorems between models of mixed choice

Abstract

We relate the so-called powercone models of mixed non-deterministic and probabilistic choice proposed by Tix, Keimel, Plotkin, Mislove, Ouaknine, Worrell, Morgan and McIver, to our own models of previsions. Under suitable topological assumptions, we show that they are isomorphic. We rely on Keimel's cone-theoretic variants of the classical Hahn–Banach separation theorems, using functional analytic methods, and on the Schröder–Simpson Theorem.