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 |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=86872413&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 86872413 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00224812 3TY jtl: Journal of Symbolic Logic issn: 00224812 maglogo: N pubinfo: dt: Mar2013 vid: 78 iid: 1 pid: 15979 pub: Cambridge University Press artinfo: ui: 86872413 10.2178/jsl.7801070 ppf: 101 ppct: 12 formats: tig: 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 refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2013 holdings: @attributes: islocal: N |
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