2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73954We construct a measure on omega-one^2 over the ground model in the forcing extension of a measure algebra, and investigate when measure theoretic properties of some measurable colouring of omega-one^2 imply the existence of an uncountable subset of omega-one whose square is homogeneous. This gives a new proof of the fact that, under a suitable axiomatic assumption, there are no Souslin (omega-one,omega-one) gaps in the Boolean algebra L^0(nu)/Fin when nu is a separable measure.Proceedings of the Kyoto conference on Forcing Method and Large Cardinals, 2004LogicClassical Analysis and ODEstext