Submission date: 20 September 2007

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.

Mathematics Subject Classification: 03C60, 12E99

Keywords and phrases: algebraic closure in fields, independence relations, henselian fields

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