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Groupes Fins

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Milliet_0-280478.pdf
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2014

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http://nbn-resolving.de/urn:nbn:de:bsz:352-0-280478
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https://doi.org/10.1017/jsl.2014.12
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The Journal of Symbolic Logic. 2014, 79(4), pp. 1120-1132. ISSN 0022-4812. eISSN 1943-5886. Available under: doi: 10.1017/jsl.2014.12

Zusammenfassung

We investigate some common points between stable structures and weakly small structures and define a structure M to be fine if the Cantor-Bendixson rank of the topological space Sφ(dcleq(A)) is an ordinal for every finite subset A of M and every formula φ(x.y) where x is of arity 1. By definition, a theory is fine if all its models are so. Stable theories and small theories are fine, and weakly minimal structures are fine. For any finite subset A of a fine group G, the traces on the algebraic closure acl(A) of A of definable subgroups of G over acl(A) which are boolean combinations of instances of an arbitrary fixed formula can decrease only finitely many times. An infinite field with a fine theory has no additive nor multiplicative proper definable subgroups of finite index, nor Artin-Schreier extensions.

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Fachgebiet (DDC)
510 Mathematik

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Model theory, Cantor-Bendixson rank, local descending chain condition, Artin-Schreier extension

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undefined / . - undefined, undefined

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ISO 690MILLIET, Cedric, 2014. Groupes Fins. In: The Journal of Symbolic Logic. 2014, 79(4), pp. 1120-1132. ISSN 0022-4812. eISSN 1943-5886. Available under: doi: 10.1017/jsl.2014.12
BibTex
@article{Milliet2014Group-30526,
  year={2014},
  doi={10.1017/jsl.2014.12},
  title={Groupes Fins},
  number={4},
  volume={79},
  issn={0022-4812},
  journal={The Journal of Symbolic Logic},
  pages={1120--1132},
  author={Milliet, Cedric}
}
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