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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.<\/jats:p>","DOI":"10.2178\/jsl\/1268917491","type":"journal-article","created":{"date-parts":[[2010,3,18]],"date-time":"2010-03-18T13:05:57Z","timestamp":1268917557000},"page":"481-500","source":"Crossref","is-referenced-by-count":16,"title":["Schlanke K\u00f6rper (Slim fields)"],"prefix":"10.1017","volume":"75","author":[{"given":"Markus","family":"Junker","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jochen","family":"Koenigsmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002644_ref017","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1959-0112842-7"},{"key":"S0022481200002644_ref016","first-page":"318","article-title":"Model theoretic methods in the theory of topological fields","volume":"299","author":"Prestel","year":"1978","journal-title":"Journal f\u00fcr die Reine und Angewandte Mathematik"},{"key":"S0022481200002644_ref012","first-page":"947","volume":"67","author":"Koenigsmann","year":"2002","journal-title":"Defining transcendentals in function fields"},{"key":"S0022481200002644_ref010","first-page":"326","volume":"67","author":"Junker","year":"2002","journal-title":"Theories with equational forking"},{"key":"S0022481200002644_ref008","first-page":"1125","volume":"48","author":"Jarden","year":"1983","journal-title":"Model-complete theories of e-free Ax fields"},{"key":"S0022481200002644_ref006","unstructured":"Fehm Arno , Subfields of ample fields I. 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