Some partition properties for measurable colourings of omega-one^2
Logic
2007-05-23 v1 Classical Analysis and ODEs
Abstract
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.
Keywords
Cite
@article{arxiv.math/0501421,
title = {Some partition properties for measurable colourings of omega-one^2},
author = {James Hirschorn},
journal= {arXiv preprint arXiv:math/0501421},
year = {2007}
}
Comments
Proceedings of the Kyoto conference on Forcing Method and Large Cardinals, 2004