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...

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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
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Zusammenfassung: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.
ISSN:0022-4812
1943-5886
DOI:10.2178/jsl/1268917491