2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69132I prove forcing preservation theorems for products of definable partial orders preserving the cofinality of the meager or null ideal. Rectangular Ramsey theorems for related ideals follow from the proofs.16 pagesLogicCombinatorics03E60, 03E17, 03E02text