Some partition properties for measurable colourings of omega-one2
Abstract
We construct a measure on omega-one2 over the ground model in the forcing extension of a measure algebra, and investigate when measure theoretic properties of some measurable colouring of omega-one2 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 L0(nu)/Fin when nu is a separable measure.
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