On a diophantine representation of the predicate of provability

Lade...
Vorschaubild
Dateien
Zu diesem Dokument gibt es keine Dateien.
Datum
2014
Autor:innen
Moroz, Boris Zelikovich
Herausgeber:innen
Kontakt
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
URI (zitierfähiger Link)
ArXiv-ID
Internationale Patentnummer
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Core Facility der Universität Konstanz
Gesperrt bis
Titel in einer weiteren Sprache
Forschungsvorhaben
Organisationseinheiten
Zeitschriftenheft
Publikationstyp
Zeitschriftenartikel
Publikationsstatus
Published
Erschienen in
Journal of Mathematical Sciences. 2014, 199(1), pp. 36-52. ISSN 1072-3374. eISSN 1573-8795. Available under: doi: 10.1007/s10958-014-1830-2
Zusammenfassung

Let P be the first-order predicate calculus with a single binary predicate letter. Making use of the techniques of Diophantine coding developed in the works on Hilbert’s tenth problem, we construct a polynomial F(t; x1, . . . , xn) with integral rational coefficients such that the Diophantine equation
F(t0;x1,…, xn)=0
is soluble in integers if and only if the formula of P numbered t0 in the chosen numbering of the formulas of P is provable in P. As an application of that construction, we describe a class of Diophantine equations that can be proved insoluble only under some additional axioms of the axiomatic set theory, for instance, assuming the existence of an inaccessible cardinal. Bibliography: 14 titles.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
Konferenz
Rezension
undefined / . - undefined, undefined
Zitieren
ISO 690CARL, Merlin, Boris Zelikovich MOROZ, 2014. On a diophantine representation of the predicate of provability. In: Journal of Mathematical Sciences. 2014, 199(1), pp. 36-52. ISSN 1072-3374. eISSN 1573-8795. Available under: doi: 10.1007/s10958-014-1830-2
BibTex
@article{Carl2014dioph-21343.2,
  year={2014},
  doi={10.1007/s10958-014-1830-2},
  title={On a diophantine representation of the predicate of provability},
  number={1},
  volume={199},
  issn={1072-3374},
  journal={Journal of Mathematical Sciences},
  pages={36--52},
  author={Carl, Merlin and Moroz, Boris Zelikovich}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/21343.2">
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:creator>Moroz, Boris Zelikovich</dc:creator>
    <dc:rights>terms-of-use</dc:rights>
    <dc:language>eng</dc:language>
    <dc:contributor>Carl, Merlin</dc:contributor>
    <dcterms:title>On a diophantine representation of the predicate of provability</dcterms:title>
    <dcterms:abstract xml:lang="eng">Let P be the first-order predicate calculus with a single binary predicate letter. Making use of the techniques of Diophantine coding developed in the works on Hilbert’s tenth problem, we construct a polynomial F(t; x1, . . . , xn) with integral rational coefficients such that the Diophantine equation&lt;br /&gt;F(t&lt;sub&gt;0&lt;/sub&gt;;x&lt;sub&gt;1&lt;/sub&gt;,…, x&lt;sub&gt;n&lt;/sub&gt;)=0&lt;br /&gt;is soluble in integers if and only if the formula of P numbered t0 in the chosen numbering of the formulas of P is provable in P. As an application of that construction, we describe a class of Diophantine equations that can be proved insoluble only under some additional axioms of the axiomatic set theory, for instance, assuming the existence of an inaccessible cardinal. Bibliography: 14 titles.</dcterms:abstract>
    <dc:contributor>Moroz, Boris Zelikovich</dc:contributor>
    <dcterms:issued>2014</dcterms:issued>
    <dc:creator>Carl, Merlin</dc:creator>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-02-05T14:52:02Z</dc:date>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-02-05T14:52:02Z</dcterms:available>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/21343.2"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
  </rdf:Description>
</rdf:RDF>
Interner Vermerk
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Kontakt
URL der Originalveröffentl.
Prüfdatum der URL
Prüfungsdatum der Dissertation
Finanzierungsart
Kommentar zur Publikation
Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Ja
Begutachtet
Diese Publikation teilen

Versionsgeschichte

Gerade angezeigt 1 - 2 von 2
VersionDatumZusammenfassung
2*
2018-02-05 09:25:51
2013-02-19 10:27:46
* Ausgewählte Version