BOUNDING HOMOGENEOUS MODELS.

A Turing degree d is homogeneous bounding if every complete decidable (CD) theory has a d-decidable homogeneous model A, i.e., the elementary diagram D(A) has degree d. It follows from results of Macintyre and Marker that every PA degree (i.e., every degree of a complete extension of Peano Arithmeti...

Descripción completa

Detalles Bibliográficos
Publicado en:Journal of Symbolic Logic Vol. 72; no. 1; pp. 305 - 324
Autores principales: Csima, Barbara F., Harizanov, Valentina S., Hirschfeldt, Denis R., Soare, Robert I.
Formato: Artículo
Publicado: Cambridge University Press Mar2007
Materias:
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=24665170&site=ehost-live
header:
  @attributes:
    shortDbName: hlh
    uiTerm: 24665170
    longDbName: Humanities International Complete
    uiTag: AN
  controlInfo:
    bkinfo:
    jinfo:
      jid:
        00224812
        3TY
      jtl: Journal of Symbolic Logic
      issn: 00224812
      maglogo: N
    pubinfo:
      dt: Mar2007
      vid: 72
      iid: 1
      pid: 15979
      pub: Cambridge University Press
    artinfo:
      ui:
        24665170
        10.2178/jsl/1174668397
      ppf: 305
      ppct: 19
      formats:
      tig:
        atl: BOUNDING HOMOGENEOUS MODELS.
      aug:
        au:
          Csima, Barbara F.
          Harizanov, Valentina S.
          Hirschfeldt, Denis R.
          Soare, Robert I.
        affil:
          Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada
          Department of Mathematics, The George Washington University, Washington, D.C. 20052, USA
          Department of Mathematics, The University of Chicago, Chicago, Illinois 60637, USA
      su:
        Turing (Computer program language)
        Computable functions
        Combinatorics
        Mathematical models
        Mathematical logic
        Recursive sequences (Mathematics)
        Recursion theory
        Abstract algebra
      sug:
        subj:
          Turing (Computer program language)
          Computable functions
          Combinatorics
          Mathematical models
          Mathematical logic
          Recursive sequences (Mathematics)
          Recursion theory
          Abstract algebra
      ab: A Turing degree d is homogeneous bounding if every complete decidable (CD) theory has a d-decidable homogeneous model A, i.e., the elementary diagram D(A) has degree d. It follows from results of Macintyre and Marker that every PA degree (i.e., every degree of a complete extension of Peano Arithmetic) is homogeneous bounding. We prove that in fact a degree is homogeneous bounding if and only if it is a PA degree. We do this by showing that there is a single CD theory T such that every homogeneous model of T has a PA degree.
      pubtype: Academic Journal
      doctype: Article
      src: R
    language: English
    refInfo:
    copyright:
      @attributes:
        flag: Y
      dt:
        @attributes:
          year: 2007
    holdings:
      @attributes:
        islocal: N