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...

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Publicado en:Journal of Symbolic Logic Vol. 78; no. 1; pp. 101 - 113
Autor principal: CONLEY, CLINTON T.
Formato: Artículo
Publicado: Cambridge University Press Mar2013
Materias:
Acceso en línea:Ver este registro en EBSCOhost
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        atl: CANONIZING RELATIONS ON NONSMOOTH SETS.
      aug:
        au: CONLEY, CLINTON T.
        affil:
          KURT GÖDEL RESEARCH CENTER FOR MATHEMATICAL LOGIC, UNIVERSITY OF VIENNA, WÄHRINGER STRAßE 25, 1090 WIEN, AUSTRIA
          Department of Mathematics, Cornell University, Ithaca, NY 14853, USA
      su:
        Nonsmooth optimization
        Baire classes
        Finite difference method
        Mathematics theorems
        Homogeneous spaces
        Equivalence classes (Set theory)
      sug:
        subj:
          Nonsmooth optimization
          Baire classes
          Finite difference method
          Mathematics theorems
          Homogeneous spaces
          Equivalence classes (Set theory)
      ab: 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.
      pubtype: Academic Journal
      doctype: Article
      src: R
    language: English
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          year: 2013
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