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Die böse Farbe

Part of: Model theory

Published online by Cambridge University Press:  11 December 2007

Andreas Baudisch ,
Martin Hils ,
Amador Martin-Pizarro  and
Frank O. Wagner
Andreas Baudisch
Affiliation:
Institut für Mathematik, Humboldt-Universität zu Berlin, D-10099 Berlin, Germany (baudisch@mathematik.hu-berlin.de; hils@mathematik.hu-berlin.de).
Martin Hils
Affiliation:
Institut für Mathematik, Humboldt-Universität zu Berlin, D-10099 Berlin, Germany (baudisch@mathematik.hu-berlin.de; hils@mathematik.hu-berlin.de). Equipe de Logique Mathématique, Université Denis-Diderot Paris VII, 75251 Paris Cedex 05, France. Université de Lyon; Université Lyon 1, CNRS, Institut Camille Jordan, 43 bd du 11 nov. 1918, 69622 Villeurbanne Cedex, France, (pizarro@math.univ-lyon1.fr; wagner@math.univ-lyon1.fr).
Amador Martin-Pizarro
Affiliation:
Institut für Mathematik, Humboldt-Universität zu Berlin, D-10099 Berlin, Germany (baudisch@mathematik.hu-berlin.de; hils@mathematik.hu-berlin.de). Université de Lyon; Université Lyon 1, CNRS, Institut Camille Jordan, 43 bd du 11 nov. 1918, 69622 Villeurbanne Cedex, France, (pizarro@math.univ-lyon1.fr; wagner@math.univ-lyon1.fr).
Frank O. Wagner
Affiliation:
Université de Lyon; Université Lyon 1, CNRS, Institut Camille Jordan, 43 bd du 11 nov. 1918, 69622 Villeurbanne Cedex, France, (pizarro@math.univ-lyon1.fr; wagner@math.univ-lyon1.fr).
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Abstract

We construct a bad field in characteristic zero. That is, we construct an algebraically closed field which carries a notion of dimension analogous to Zariski-dimension, with an infinite proper multiplicative subgroup of dimension one, and such that the field itself has dimension two. This answers a longstanding open question by Zilber.

Zusammenfassung

Wir konstruieren einen schlechten Körper der Charakteristik Null. Mit anderen Worten, wir konstruieren einen algebraisch abgeschlossenen Körper mit einem Dimensionsbegriff analog der Zariski-Dimension, zusammen mit einer unendlichen echten multiplikativen Untergruppe der Dimension Eins, so daβ der Körper selbst Dimension Zwei hat. Dies beantwortet eine alte Frage von Zilber.

Keywords

ModelltheorieKörper von endlichem MorleyrangSchlechter KörperAmalgamierungskonstruktionmodel theoryfields of finite Morley rankbad fieldamalgamation construction

MSC classification

Secondary: 03C65: Models of other mathematical theories 03C50: Models with special properties (saturated, rigid, etc.) 03C45: Classification theory, stability and related concepts 03C35: Categoricity and completeness of theories
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 8 , Issue 3 , July 2009 , pp. 415 - 443
Copyright
Copyright © Cambridge University Press 2009

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