Kim–Pillay Characterization for Affine Logic

Establish whether affine logic admits a theorem of Kim and Pillay characterizing simple affine theories by an independence relation on extremal types.

Background

The paper concludes by considering affine logic, where models can be represented through direct integrals of extremal models and where formulas are affine combinations. It recalls that the classical Kim–Pillay theorem characterizes simplicity through an independence relation satisfying structural axioms.

Whether an analogous characterization exists in affine logic is left open. The proposed analogue would formulate independence on extremal types and identify the conditions under which an affine theory is simple.