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March 2013 Fields with few types
Cédric Milliet
J. Symbolic Logic 78(1): 72-84 (March 2013). DOI: 10.2178/jsl.7801050

Abstract

According to 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.

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Cédric Milliet. "Fields with few types." J. Symbolic Logic 78 (1) 72 - 84, March 2013. https://doi.org/10.2178/jsl.7801050

Information

Published: March 2013
First available in Project Euclid: 23 January 2013

zbMATH: 1309.03015
MathSciNet: MR3087062
Digital Object Identifier: 10.2178/jsl.7801050

Subjects:
Primary: 03C45, 03C60

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 1 • March 2013
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