Schlanke Körper (Slim fields)

Schlanke Körper (Slim fields)

We examine fields in which model theoretic algebraic closure coincides with relative field theoretic algebraic closure. These are perfect fields with nice model theoretic behaviour. For example, they are exactly the fields in which algebraic independence is an abstract independence relation in the s...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:The Journal of symbolic logic 2010-06, Vol.75 (2), p.481-500
Hauptverfasser: Junker, Markus, Koenigsmann, Jochen
Format: Artikel
Sprache:eng
Schlagworte:
Abstract algebra
Algebra
Algebraic topology
Automorphisms
Axioms
Coefficients
Mathematical rings
Mathematical theorems
Polynomials
Transcendentals
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 500
container_issue 2
container_start_page 481
container_title The Journal of symbolic logic
container_volume 75
creator Junker, Markus
Koenigsmann, Jochen
description We examine fields in which model theoretic algebraic closure coincides with relative field theoretic algebraic closure. These are perfect fields with nice model theoretic behaviour. For example, they are exactly the fields in which algebraic independence is an abstract independence relation in the sense of Kim and Pillay. Classes of examples are perfect PAC fields, model complete large fields and henselian valued fields of characteristic 0.
doi_str_mv 10.2178/jsl/1268917491
format Article
fullrecord <record><control><sourceid>jstor_proje</sourceid><recordid>TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_jsl_1268917491</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>25676793</jstor_id><sourcerecordid>25676793</sourcerecordid><originalsourceid>FETCH-LOGICAL-c396t-9c521dd8f16cbc2ed9dafabc44fec4c41c04a87c16be70e059a5dfdb5e7092e23</originalsourceid><addsrcrecordid>eNplUMtOwzAQtBBIlMKVG6hHOKS1HT9voIgWSiRES8-W44dImpLKDhL8GD_AjxGUqhw4jXZnZ0azAJwjOMaIi0kV6wnCTEjEiUQHYIAkSRMqBDsEAwgxTohA-BicxFhBCKkkYgAul-a11m9rN3r8_gpbF0ZXy7rcjHzpahuvT8GR13V0ZzscgtX07iW7T_Kn2UN2mycmlaxNpKEYWSs8YqYw2FlptdeFIcQ7QwxBBhItuEGscBy6LltT621Bu0lih9MhuOl9t6GpnGndu6lLq7ah3OjwqRpdqmyV77Y76Pqqv76dxbi3MKGJMTi_VyOofh_0X3DRC6rYNmF_jSnjjMu045OeL2PrPva8DmvFeMqpYrNnlWXzxXTBsJqnP8Tlct0</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Schlanke Körper (Slim fields)</title><source>JSTOR Mathematics &amp; Statistics</source><source>Jstor Complete Legacy</source><creator>Junker, Markus ; Koenigsmann, Jochen</creator><creatorcontrib>Junker, Markus ; Koenigsmann, Jochen</creatorcontrib><description>We examine fields in which model theoretic algebraic closure coincides with relative field theoretic algebraic closure. These are perfect fields with nice model theoretic behaviour. For example, they are exactly the fields in which algebraic independence is an abstract independence relation in the sense of Kim and Pillay. Classes of examples are perfect PAC fields, model complete large fields and henselian valued fields of characteristic 0.</description><identifier>ISSN: 0022-4812</identifier><identifier>EISSN: 1943-5886</identifier><identifier>DOI: 10.2178/jsl/1268917491</identifier><language>eng</language><publisher>New York, USA: Cambridge University Press</publisher><subject>Abstract algebra ; Algebra ; Algebraic topology ; Automorphisms ; Axioms ; Coefficients ; Mathematical rings ; Mathematical theorems ; Polynomials ; Transcendentals</subject><ispartof>The Journal of symbolic logic, 2010-06, Vol.75 (2), p.481-500</ispartof><rights>Copyright © 2010 Association for Symbolic Logic</rights><rights>Copyright 2010 Association for Symbolic Logic</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c396t-9c521dd8f16cbc2ed9dafabc44fec4c41c04a87c16be70e059a5dfdb5e7092e23</citedby><cites>FETCH-LOGICAL-c396t-9c521dd8f16cbc2ed9dafabc44fec4c41c04a87c16be70e059a5dfdb5e7092e23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/25676793$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/25676793$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,776,780,799,828,881,27903,27904,57996,58000,58229,58233</link.rule.ids></links><search><creatorcontrib>Junker, Markus</creatorcontrib><creatorcontrib>Koenigsmann, Jochen</creatorcontrib><title>Schlanke Körper (Slim fields)</title><title>The Journal of symbolic logic</title><description>We examine fields in which model theoretic algebraic closure coincides with relative field theoretic algebraic closure. These are perfect fields with nice model theoretic behaviour. For example, they are exactly the fields in which algebraic independence is an abstract independence relation in the sense of Kim and Pillay. Classes of examples are perfect PAC fields, model complete large fields and henselian valued fields of characteristic 0.</description><subject>Abstract algebra</subject><subject>Algebra</subject><subject>Algebraic topology</subject><subject>Automorphisms</subject><subject>Axioms</subject><subject>Coefficients</subject><subject>Mathematical rings</subject><subject>Mathematical theorems</subject><subject>Polynomials</subject><subject>Transcendentals</subject><issn>0022-4812</issn><issn>1943-5886</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNplUMtOwzAQtBBIlMKVG6hHOKS1HT9voIgWSiRES8-W44dImpLKDhL8GD_AjxGUqhw4jXZnZ0azAJwjOMaIi0kV6wnCTEjEiUQHYIAkSRMqBDsEAwgxTohA-BicxFhBCKkkYgAul-a11m9rN3r8_gpbF0ZXy7rcjHzpahuvT8GR13V0ZzscgtX07iW7T_Kn2UN2mycmlaxNpKEYWSs8YqYw2FlptdeFIcQ7QwxBBhItuEGscBy6LltT621Bu0lih9MhuOl9t6GpnGndu6lLq7ah3OjwqRpdqmyV77Y76Pqqv76dxbi3MKGJMTi_VyOofh_0X3DRC6rYNmF_jSnjjMu045OeL2PrPva8DmvFeMqpYrNnlWXzxXTBsJqnP8Tlct0</recordid><startdate>20100601</startdate><enddate>20100601</enddate><creator>Junker, Markus</creator><creator>Koenigsmann, Jochen</creator><general>Cambridge University Press</general><general>Association for Symbolic Logic, Inc</general><general>Association for Symbolic Logic</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20100601</creationdate><title>Schlanke Körper (Slim fields)</title><author>Junker, Markus ; Koenigsmann, Jochen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c396t-9c521dd8f16cbc2ed9dafabc44fec4c41c04a87c16be70e059a5dfdb5e7092e23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Abstract algebra</topic><topic>Algebra</topic><topic>Algebraic topology</topic><topic>Automorphisms</topic><topic>Axioms</topic><topic>Coefficients</topic><topic>Mathematical rings</topic><topic>Mathematical theorems</topic><topic>Polynomials</topic><topic>Transcendentals</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Junker, Markus</creatorcontrib><creatorcontrib>Koenigsmann, Jochen</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><jtitle>The Journal of symbolic logic</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Junker, Markus</au><au>Koenigsmann, Jochen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Schlanke Körper (Slim fields)</atitle><jtitle>The Journal of symbolic logic</jtitle><date>2010-06-01</date><risdate>2010</risdate><volume>75</volume><issue>2</issue><spage>481</spage><epage>500</epage><pages>481-500</pages><issn>0022-4812</issn><eissn>1943-5886</eissn><abstract>We examine fields in which model theoretic algebraic closure coincides with relative field theoretic algebraic closure. These are perfect fields with nice model theoretic behaviour. For example, they are exactly the fields in which algebraic independence is an abstract independence relation in the sense of Kim and Pillay. Classes of examples are perfect PAC fields, model complete large fields and henselian valued fields of characteristic 0.</abstract><cop>New York, USA</cop><pub>Cambridge University Press</pub><doi>10.2178/jsl/1268917491</doi><tpages>20</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0022-4812
ispartof The Journal of symbolic logic, 2010-06, Vol.75 (2), p.481-500
issn 0022-4812
1943-5886
language eng
recordid cdi_projecteuclid_primary_oai_CULeuclid_euclid_jsl_1268917491
source JSTOR Mathematics & Statistics; Jstor Complete Legacy
subjects Abstract algebra
Algebra
Algebraic topology
Automorphisms
Axioms
Coefficients
Mathematical rings
Mathematical theorems
Polynomials
Transcendentals
title Schlanke Körper (Slim fields)
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-23T09%3A22%3A20IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proje&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Schlanke%20K%C3%B6rper%20(Slim%20fields)&rft.jtitle=The%20Journal%20of%20symbolic%20logic&rft.au=Junker,%20Markus&rft.date=2010-06-01&rft.volume=75&rft.issue=2&rft.spage=481&rft.epage=500&rft.pages=481-500&rft.issn=0022-4812&rft.eissn=1943-5886&rft_id=info:doi/10.2178/jsl/1268917491&rft_dat=%3Cjstor_proje%3E25676793%3C/jstor_proje%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=25676793&rfr_iscdi=true