Groupes Fins

Milliet, Cedric

doi:10.1017/jsl.2014.12

Groupes Fins

Publikationstyp:	Zeitschriftenartikel
URI (zitierfähiger Link):	http://nbn-resolving.de/urn:nbn:de:bsz:352-0-280478
Autor/innen:	Milliet, Cedric
Erscheinungsjahr:	2014
Erschienen in:	The Journal of Symbolic Logic ; 79 (2014), 4. - S. 1120-1132. - ISSN 0022-4812. - eISSN 1943-5886
DOI (zitierfähiger Link):	https://dx.doi.org/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(dcl^eq(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.
Fachgebiet (DDC):	510 Mathematik
Schlagwörter:	Model theory, Cantor-Bendixson rank, local descending chain condition, Artin-Schreier extension
Link zur Lizenz:	Nutzungsbedingungen
Universitätsbibliographie:	Ja
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MILLIET, Cedric, 2014. Groupes Fins. In: The Journal of Symbolic Logic. 79(4), pp. 1120-1132. ISSN 0022-4812. eISSN 1943-5886. Available under: doi: 10.1017/jsl.2014.12

@article{Milliet2014Group-30526, title={Groupes Fins}, year={2014}, doi={10.1017/jsl.2014.12}, number={4}, volume={79}, issn={0022-4812}, journal={The Journal of Symbolic Logic}, pages={1120--1132}, author={Milliet, Cedric} }

2015-03-24T15:22:52Z Groupes Fins 2014 eng Milliet, Cedric Milliet, Cedric terms-of-use 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(dcl<sup>eq</sup>(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. 2015-03-24T15:22:52Z