This question is prompted by a paper by Andre Kornell that just appeared on the arXiv. A large portion of the paper is devoted to showing that a surprising amount of ordinary mathematics can be developed in Chang's model. Although the axiom of choice does not hold in this model, weaker choice principles are available which apparently suffice for most mainstream uses.

The development is motivated by the author's view that a general theory of "quantum sets" works better in Chang's model. I suppose the fact that every set of reals is Lebesgue measurable could already be cited as a way in which the model is better from the point of view of mainstream math.

Has there been any previous work in this direction, specifically about ordinary mathematics in Chang's model? (Comments about what is known to follow from known properties of the model, e.g., the axiom of determinacy plus dependent choice, are also welcome.)