Fields with few types

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2014
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The Journal of Symbolic Logic. 2014, 78(01), pp. 72-84. ISSN 0022-4812. Available under: doi: 10.2178/jsl.7801050
Zusammenfassung

According to O. Belegradek, a first order structure is weakly small if there are countably many 1-types over any of its finite subset. We show the following results. A field extension of finite degree of an infinite weakly small field has no Artin-Schreier extension. A weakly small field of characteristic 2 is finite or algebraically closed. A weakly small division ring of positive characteristic is locally finite dimensional over its centre. A weakly small division ring of characteristic 2 is a field.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
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Small, weakly small, field, Artin-Schreier extension, Cantor-Bendixson rank, local descending chain condition.
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ISO 690MILLIET, Cedric, 2014. Fields with few types. In: The Journal of Symbolic Logic. 2014, 78(01), pp. 72-84. ISSN 0022-4812. Available under: doi: 10.2178/jsl.7801050
BibTex
@article{Milliet2014Field-26608,
  year={2014},
  doi={10.2178/jsl.7801050},
  title={Fields with few types},
  number={01},
  volume={78},
  issn={0022-4812},
  journal={The Journal of Symbolic Logic},
  pages={72--84},
  author={Milliet, Cedric}
}
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