I think that there might be significantly more that can be said about Cartesian frames that are a “partition into rectangles” than can be said about Cartesian frames in general.
By a “partition into rectangles,” I mean a Cartesian frame (A,E,⋅) such that if a0⋅e0=a1⋅e1, then a0⋅e0=a0⋅e1. In particular, this assumption is saying something to the effect of “the level of description of this world is refined enough to play nicely with the factorization into A and E.”
Frames that are partitions into rectangles
I think that there might be significantly more that can be said about Cartesian frames that are a “partition into rectangles” than can be said about Cartesian frames in general.
By a “partition into rectangles,” I mean a Cartesian frame (A,E,⋅) such that if a0⋅e0=a1⋅e1, then a0⋅e0=a0⋅e1. In particular, this assumption is saying something to the effect of “the level of description of this world is refined enough to play nicely with the factorization into A and E.”