TITLE: Ordinary mathematics in Chang's model
QUESTION [13 upvotes]: 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.)

REPLY [13 votes]: I don't have enough reputation to comment, so I'm posting my reply to François as an answer. It is possible that these results can be established from $ZF+AC_{ae}+DC+LM+BP+PSP$, but I don't make this claim. I work in a transitive model of this theory that is closed under countable sequences, or equivalently under countable unions, which implies that certain functional-analytic properties, such as the completeness of a metric space, are absolute. We can often verify a familiar fact by appealing to absoluteness, and this is typically much faster than checking its proof down to first principles. For most individual results, this is a matter of convenience, but for research in an established research area, this is effectively a necessity.