Continuous-logic analogues of the main saturation and non-saturation results

Establish analogues of the paper’s main results on saturation and non-saturation of reduced products for structures in continuous model theory, including the counterparts for products over Fin and layered ideals when the reduced product’s theory is stable or unstable.

Background

While many arguments have counterparts in continuous logic, proofs are more technical and often rely on continuous versions of Feferman–Vaught and Palyutin-type results. The authors suggest that analogous saturation phenomena should hold for metric structures.

Confirming these analogues would extend the scope of the paper’s classification of saturation behavior, bridging discrete and continuous frameworks.