Some partition properties for measurable colourings of omega-one^2

Details Some partition properties for measurable colourings of omega-one^2 Some partition properties for measurable colourings of omega-one^2

2005-01-24

arxiv.org/abs/math/0501421v1

Mathematics

Logic

Proceedings of the Kyoto conference on Forcing Method and Large Cardinals, 2004

Scientific paper

We 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.

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