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...
| Publicado en: | Journal of Symbolic Logic Vol. 72; no. 1; pp. 305 - 324 |
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| Autores principales: | , , , |
| Formato: | Artículo |
| Publicado: |
Cambridge University Press
Mar2007
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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=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 |
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