## Fields with few types

2014
Journal article
##### Published in
The Journal of Symbolic Logic ; 78 (2014), 01. - pp. 72-84. - ISSN 0022-4812
##### Abstract
According to O. Belegradek, a first order structure is weakly small if there are countably many 1-types over any of its finite subset. We show the following results. A field extension of finite degree of an infinite weakly small field has no Artin-Schreier extension. A weakly small field of characteristic 2 is finite or algebraically closed. A weakly small division ring of positive characteristic is locally finite dimensional over its centre. A weakly small division ring of characteristic 2 is a field.
510 Mathematics
##### Keywords
Small,weakly small,field,Artin-Schreier extension,Cantor-Bendixson rank,local descending chain condition.
##### Cite This
ISO 690MILLIET, Cedric, 2014. Fields with few types. In: The Journal of Symbolic Logic. 78(01), pp. 72-84. ISSN 0022-4812. Available under: doi: 10.2178/jsl.7801050
BibTex
@article{Milliet2014Field-26608,
year={2014},
doi={10.2178/jsl.7801050},
title={Fields with few types},
number={01},
volume={78},
issn={0022-4812},
journal={The Journal of Symbolic Logic},
pages={72--84},
author={Milliet, Cedric}
}

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#" >
<foaf:homepage rdf:resource="http://localhost:8080/"/>
<dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/26608/2/Milliet_266083.pdf"/>
<dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
<dcterms:issued>2014</dcterms:issued>
<dc:contributor>Milliet, Cedric</dc:contributor>
<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">2014-02-27T12:36:45Z</dcterms:available>
<bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/26608"/>
<dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2014-02-27T12:36:45Z</dc:date>
<dc:creator>Milliet, Cedric</dc:creator>
<dc:rights>terms-of-use</dc:rights>
<dcterms:abstract xml:lang="eng">According to O. Belegradek, a first order structure is weakly small if there are countably many 1-types over any of its finite subset. We show the following results. A field extension of finite degree of an infinite weakly small field has no Artin-Schreier extension. A weakly small field of characteristic 2 is finite or algebraically closed. A weakly small division ring of positive characteristic is locally finite dimensional over its centre. A weakly small division ring of characteristic 2 is a field.</dcterms:abstract>
<dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
<dcterms:bibliographicCitation>The Journal of Symbolic Logic ; 78 (2013), 1. - S. 72-84</dcterms:bibliographicCitation>
<dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/26608/2/Milliet_266083.pdf"/>
<dc:language>eng</dc:language>
<dcterms:title>Fields with few types</dcterms:title>
</rdf:Description>
</rdf:RDF>

Yes