Publikation: 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
Schlagwörter
Small, weakly small, field, Artin-Schreier extension, Cantor-Bendixson rank, local descending chain condition.
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MILLIET, 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.7801050BibTex
@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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<dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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