Journal of Symbolic Logic 75 (2):481-500 (2010)

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
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DOI 10.2178/jsl/1268917491
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Simple Theories.Byunghan Kim & Anand Pillay - 1996 - Annals of Pure and Applied Logic 88 (2):149-164.
Properties and Consequences of Thorn-Independence.Alf Onshuus - 2006 - Journal of Symbolic Logic 71 (1):1 - 21.
Fundamentals of Forking.Victor Harnik & Leo Harrington - 1984 - Annals of Pure and Applied Logic 26 (3):245-286.
Model-Complete Theories of Pseudo-Algebraically Closed Fields.William H. Wheeler - 1979 - Annals of Mathematical Logic 17 (3):205-226.
A Note on Equational Theories.Markus Junker - 2000 - Journal of Symbolic Logic 65 (4):1705-1712.

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