CANONIZING RELATIONS ON NONSMOOTH SETS.
We show that any symmetric, Baire measurable function from the complement of E to a finite set is constant on an E-nonsmooth square. A simultaneous generalization of Galvin's theorem that Baire measurable colorings admit perfect homogeneous sets and the Kanovei-Zapletal theorem canonizing Borel equi...
| Publicado en: | Journal of Symbolic Logic Vol. 78; no. 1; pp. 101 - 113 |
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| Formato: | Artículo |
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Cambridge University Press
Mar2013
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| Acceso en línea: | Ver este registro en EBSCOhost |
| Sumario: | We show that any symmetric, Baire measurable function from the complement of E to a finite set is constant on an E-nonsmooth square. A simultaneous generalization of Galvin's theorem that Baire measurable colorings admit perfect homogeneous sets and the Kanovei-Zapletal theorem canonizing Borel equivalence relations on E-nonsmooth sets, this result is proved by relating E-nonsmooth sets to embeddings of the complete binary tree into itself and appealing to a version of Hindman's theorem on the complete binary tree. We also establish several canonization theorems which follow from the main result. |
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