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Schlanke Körper (Slim fields)

Published online by Cambridge University Press:  12 March 2014

Markus Junker  and
Jochen Koenigsmann
Markus Junker
Affiliation:
Mathematisches Institut, Eckerstrasse 1, 79104 Freiburg, Germany. E-mail: markus.junker@math.uni-freiburg.de
Jochen Koenigsmann
Affiliation:
Mathematical Institute, 24-29 St Giles', Oxford Ox1 3Lb, UK. E-mail: koenigsmann@maths.ox.ac.uk
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 2 , June 2010 , pp. 481 - 500
Copyright
Copyright © Association for Symbolic Logic 2010

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