Publikation:

CONNECTEDNESS IN STRUCTURES ON THE REAL NUMBERS: O-MINIMALITY AND UNDECIDABILITY

Lade...
Vorschaubild

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2022

Autor:innen

Dolich, Alfred
Miller, Chris
Thamrongthanyalak, Athipat

Herausgeber:innen

Kontakt

ISSN der Zeitschrift

Electronic ISSN

ISBN

Bibliografische Daten

Verlag

Schriftenreihe

Auflagebezeichnung

URI (zitierfähiger Link)
DOI (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

Publikationstyp
Zeitschriftenartikel
Publikationsstatus
Published

Erschienen in

The Journal of Symbolic Logic. Cambridge University Press on behalf of the Association for Symbolic Logic. 2022, 87(3), pp. 1243-1259. ISSN 0022-4812. eISSN 1943-5886. Available under: doi: 10.1017/jsl.2022.16

Zusammenfassung

We initiate an investigation of structures on the set of real numbers having the property that path components of definable sets are definable. All o-minimal structures on (R, <) have the property, as do all expansions of (R, +, ·, N). Our main analytic-geometric result is that any such expansion of (R, <, +) by Boolean combinations of open sets (of any arities) either is o-minimal or defines an isomorph of (N, +, ·). We also show that any given expansion of (R, <, +, N) by subsets of Nn (n allowed to vary) has the property if and only if it defines all arithmetic sets. Variations arise by considering connected components or quasicomponents instead of path components.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Konferenz

Rezension
undefined / . - undefined, undefined

Forschungsvorhaben

Organisationseinheiten

Zeitschriftenheft

Zugehörige Datensätze in KOPS

Zitieren

ISO 690DOLICH, Alfred, Chris MILLER, Alex SAVATOVSKY, Athipat THAMRONGTHANYALAK, 2022. CONNECTEDNESS IN STRUCTURES ON THE REAL NUMBERS: O-MINIMALITY AND UNDECIDABILITY. In: The Journal of Symbolic Logic. Cambridge University Press on behalf of the Association for Symbolic Logic. 2022, 87(3), pp. 1243-1259. ISSN 0022-4812. eISSN 1943-5886. Available under: doi: 10.1017/jsl.2022.16
BibTex
@article{Dolich2022CONNE-58617,
  year={2022},
  doi={10.1017/jsl.2022.16},
  title={CONNECTEDNESS IN STRUCTURES ON THE REAL NUMBERS: O-MINIMALITY AND UNDECIDABILITY},
  number={3},
  volume={87},
  issn={0022-4812},
  journal={The Journal of Symbolic Logic},
  pages={1243--1259},
  author={Dolich, Alfred and Miller, Chris and Savatovsky, Alex and Thamrongthanyalak, Athipat}
}
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/123456789/58617">
    <dc:contributor>Miller, Chris</dc:contributor>
    <dc:creator>Miller, Chris</dc:creator>
    <dc:contributor>Thamrongthanyalak, Athipat</dc:contributor>
    <dc:creator>Dolich, Alfred</dc:creator>
    <dcterms:issued>2022</dcterms:issued>
    <dcterms:abstract xml:lang="eng">We initiate an investigation of structures on the set of real numbers having the property that path components of definable sets are definable. All o-minimal structures on (R, &lt;) have the property, as do all expansions of (R, +, ·, N). Our main analytic-geometric result is that any such expansion of (R, &lt;, +) by Boolean combinations of open sets (of any arities) either is o-minimal or defines an isomorph of (N, +, ·). We also show that any given expansion of (R, &lt;, +, N) by subsets of N&lt;sup&gt;n&lt;/sup&gt; (n allowed to vary) has the property if and only if it defines all arithmetic sets. Variations arise by considering connected components or quasicomponents instead of path components.</dcterms:abstract>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/58617"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dcterms:title>CONNECTEDNESS IN STRUCTURES ON THE REAL NUMBERS: O-MINIMALITY AND UNDECIDABILITY</dcterms:title>
    <dc:contributor>Dolich, Alfred</dc:contributor>
    <dc:language>eng</dc:language>
    <dc:contributor>Savatovsky, Alex</dc:contributor>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2022-09-14T09:31:40Z</dcterms:available>
    <dc:creator>Thamrongthanyalak, Athipat</dc:creator>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2022-09-14T09:31:40Z</dc:date>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:creator>Savatovsky, Alex</dc:creator>
  </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
Nein
Begutachtet
Ja
Diese Publikation teilen