Real Closed Exponential Fields

Loading...
Thumbnail Image
Date
2011
Authors
D'Aquino, Paola
Knight, Julia F.
Lange, Karen
Editors
Contact
Journal ISSN
Electronic ISSN
ISBN
Bibliographical data
Publisher
Series
URI (citable link)
DOI (citable link)
ArXiv-ID
International patent number
Link to the license
EU project number
Project
Open Access publication
Restricted until
Title in another language
Research Projects
Organizational Units
Journal Issue
Publication type
Preprint
Publication status
Published in
Abstract
In an extended abstract Ressayre considered real closed exponential fields and integer parts that respect the exponential function. He outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre's construction, which becomes canonical once we fix the real closed exponential field, a residue field section, and a well ordering of the field. The procedure is constructible over these objects; each step looks effective, but may require many steps. We produce an example of an exponential field $R$ with a residue field $k$ and a well ordering $<$ such that $D^c(R)$ is low and $k$ and $<$ are $\Delta^0_3$, and Ressayre's construction cannot be completed in $L_{\omega_1^{CK}}$.
Summary in another language
Subject (DDC)
510 Mathematics
Keywords
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
ISO 690D'AQUINO, Paola, Julia F. KNIGHT, Salma KUHLMANN, Karen LANGE, 2011. Real Closed Exponential Fields
BibTex
@unpublished{DAquino2011Close-21245,
  year={2011},
  title={Real Closed Exponential Fields},
  author={D'Aquino, Paola and Knight, Julia F. and Kuhlmann, Salma and Lange, Karen},
  note={Also publ. in: Fundamenta Mathematicae ; 219 (2012), 2. - S. 163-190}
}
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/123456789/21245">
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:contributor>Knight, Julia F.</dc:contributor>
    <dc:language>eng</dc:language>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:contributor>Lange, Karen</dc:contributor>
    <dc:creator>Lange, Karen</dc:creator>
    <dcterms:title>Real Closed Exponential Fields</dcterms:title>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:creator>D'Aquino, Paola</dc:creator>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/21245"/>
    <dcterms:issued>2011</dcterms:issued>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/21245/1/daquino_212455.pdf"/>
    <dc:contributor>D'Aquino, Paola</dc:contributor>
    <dc:rights>terms-of-use</dc:rights>
    <dc:creator>Kuhlmann, Salma</dc:creator>
    <dcterms:abstract xml:lang="eng">In an extended abstract Ressayre considered real closed exponential fields and integer parts that respect the exponential function. He outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre's construction, which becomes canonical once we fix the real closed exponential field, a residue field section, and a well ordering of the field. The procedure is constructible over these objects; each step looks effective, but may require many steps. We produce an example of an exponential field $R$ with a residue field $k$ and a well ordering $&lt;$ such that $D^c(R)$ is low and $k$ and $&lt;$ are $\Delta^0_3$, and Ressayre's construction cannot be completed in $L_{\omega_1^{CK}}$.</dcterms:abstract>
    <dc:contributor>Kuhlmann, Salma</dc:contributor>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-02-04T09:55:24Z</dcterms:available>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dc:creator>Knight, Julia F.</dc:creator>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/21245/1/daquino_212455.pdf"/>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-02-04T09:55:24Z</dc:date>
  </rdf:Description>
</rdf:RDF>
Internal note
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Contact
URL of original publication
Test date of URL
Examination date of dissertation
Method of financing
Comment on publication
Also publ. in: Fundamenta Mathematicae ; 219 (2012), 2. - S. 163-190
Alliance license
Corresponding Authors der Uni Konstanz vorhanden
International Co-Authors
Bibliography of Konstanz
Yes
Refereed