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Some partition properties for measurable colourings of omega-one2

2005/01/24 by James Hirschorn, Hirschorn, James
Engineering · Mathematics · #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #graph theory and CDMA systems #math.CA #math.LO

paper · pdf · doi:10.48550/arxiv.math/0501421

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

arxiv created 2005/01/24 · openalex publication_date 2005/01/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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