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T-height in weakly o-minimal structures

Published online by Cambridge University Press:  12 March 2014

James Tyne
James Tyne*
Affiliation:
Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, USA.E-mail:tyne@member.ams.org
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Abstract

Given a weakly o-minimal theory T, the T-height of an element of a model of T is defined as a means of classifying the order of magnitude of the element. If T satisfies some easily met technical conditions, then this classification is coarse enough for a Wilkie-type inequality: given a set of elements of a model of T, each of which has a different T-height, the cardinality of this set is at most 1 plus the minimum cardinality of a set that generates the structure.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 3 , September 2006 , pp. 747 - 762
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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