I would not be too surprised if some other theorem in that paper was relevant, either; I haven’t gotten through enough to say, except that it’s definitely exploring related questions.
The statement Sawin proved refers to computable probability distributions over logical statements, and Gaifman & Snir only considered a class of probability distributions which are necessarily undefinable (by Tarski’s theorem, since their probability distributions are certain about the truth-values of all statements in L0, which is expressive enough to implement Peano Arithmetic). So I actually would be fairly surprised if the paper ended up containing something relevant to it.
The statement Sawin proved refers to computable probability distributions over logical statements, and Gaifman & Snir only considered a class of probability distributions which are necessarily undefinable (by Tarski’s theorem, since their probability distributions are certain about the truth-values of all statements in L0, which is expressive enough to implement Peano Arithmetic). So I actually would be fairly surprised if the paper ended up containing something relevant to it.