Definability of henselian valuations by conditions on the value group
Definability of henselian valuations by conditions on the value group
No Thumbnail Available
Files
There are no files associated with this item.
Date
2022
Editors
Journal ISSN
Electronic ISSN
ISBN
Bibliographical data
Publisher
Series
DOI (citable link)
ArXiv-ID
International patent number
Link to the license
EU project number
Project
Open Access publication
Collections
Title in another language
Publication type
Journal article
Publication status
Published
Published in
The Journal of Symbolic Logic ; 2022. - Cambridge University Press (CUP). - ISSN 0022-4812. - eISSN 1943-5886
Abstract
Given a henselian valuation, we study its definability (with and without parameters) by examining conditions on the value group. We show that any henselian valuation whose value group is not closed in its divisible hull is definable in the language of rings, using one parameter. Thereby we strengthen known definability results. Moreover, we show that in this case, one parameter is optimal in the sense that one cannot obtain definability without parameters. To this end, we present a construction method for a $t$-henselian non-henselian ordered field elementarily equivalent to a henselian field with a specified value group.
Summary in another language
Subject (DDC)
510 Mathematics
Keywords
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
ISO 690
KRAPP, Lothar Sebastian, Salma KUHLMANN, Moritz LINK, 2022. Definability of henselian valuations by conditions on the value group. In: The Journal of Symbolic Logic. Cambridge University Press (CUP). ISSN 0022-4812. eISSN 1943-5886. Available under: doi: 10.1017/jsl.2022.34BibTex
@article{Krapp2022-06-13Defin-57827, year={2022}, doi={10.1017/jsl.2022.34}, title={Definability of henselian valuations by conditions on the value group}, issn={0022-4812}, journal={The Journal of Symbolic Logic}, author={Krapp, Lothar Sebastian and Kuhlmann, Salma and Link, Moritz} }
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/123456789/57827"> <dcterms:abstract xml:lang="eng">Given a henselian valuation, we study its definability (with and without parameters) by examining conditions on the value group. We show that any henselian valuation whose value group is not closed in its divisible hull is definable in the language of rings, using one parameter. Thereby we strengthen known definability results. Moreover, we show that in this case, one parameter is optimal in the sense that one cannot obtain definability without parameters. To this end, we present a construction method for a $t$-henselian non-henselian ordered field elementarily equivalent to a henselian field with a specified value group.</dcterms:abstract> <foaf:homepage rdf:resource="http://localhost:8080/"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2022-06-22T15:10:48Z</dc:date> <dc:contributor>Kuhlmann, Salma</dc:contributor> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dc:contributor>Krapp, Lothar Sebastian</dc:contributor> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2022-06-22T15:10:48Z</dcterms:available> <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/> <dcterms:title>Definability of henselian valuations by conditions on the value group</dcterms:title> <dc:contributor>Link, Moritz</dc:contributor> <dc:creator>Link, Moritz</dc:creator> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/57827"/> <dc:rights>terms-of-use</dc:rights> <dc:creator>Kuhlmann, Salma</dc:creator> <dc:language>eng</dc:language> <dc:creator>Krapp, Lothar Sebastian</dc:creator> <dcterms:issued>2022-06-13</dcterms:issued> </rdf:Description> </rdf:RDF>
Internal note
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Examination date of dissertation
Method of financing
Comment on publication
Alliance license
Corresponding Authors der Uni Konstanz vorhanden
International Co-Authors
Bibliography of Konstanz
Yes
Refereed
Yes
Online First: Journal articles that are published online before they appear as an actual part of a journal issue. Online first articles are published on the journal's website in the publisher's version.