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CONVEXLY ORDERABLE GROUPS AND VALUED FIELDS

Published online by Cambridge University Press:  17 April 2014

JOSEPH FLENNER  and
VINCENT GUINGONA
JOSEPH FLENNER
Affiliation:
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF SAINT FRANCIS, 2701 SPRING STREET, FORT WAYNE, IN 46808, USAE-mail:jflenner@sf.edu
VINCENT GUINGONA
Affiliation:
DEPARTMENT OF MATHEMATICSUNIVERSITY OF NOTRE DAME255 HURLEY HALLNOTRE DAMEIN 46556USAE-mail:guingona.1@nd.edu, URL:http://www.nd.edu/∼vguingon/
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Abstract

We consider the model theoretic notion of convex orderability, which fits strictly between the notions of VC-minimality and dp-minimality. In some classes of algebraic theories, however, we show that convex orderability and VC-minimality are equivalent, and use this to give a complete classification of VC-minimal theories of ordered groups and abelian groups. Consequences for fields are also considered, including a necessary condition for a theory of valued fields to be quasi-VC-minimal. For example, the p-adics are not quasi-VC-minimal.

Keywords

Convexly orderableVC-minimalityordered groupsvalued fieldsabelian groups
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 1 , March 2014 , pp. 154 - 170
Copyright
Copyright © Association for Symbolic Logic 2014 

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References

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