Pseudofinite primitive permutation groups acting on one-dimensional sets

Working in a theory with an integer-valued dimension on interpretable sets, we classify pseudofinite definably primitive permutation groups acting on one-dimensional sets which satisfy a version of chain condition on centralizers and on pointwise stabilizers. This generalizes the classification of pseudofinite definably primitive permutation groups acting on a rank 1 set in supersimple theories of finite rank, due to Elwes et al. (2011), to supersimple theories of infinite rank.