Abstract

AbstractGiven a weakly o-minimal theoryT, theT-height of an element of a model ofTis defined as a means of classifying the order of magnitude of the element. IfTsatisfies some easily met technical conditions, then this classification is coarse enough for a Wilkie-type inequality: given a set of elements of a model ofT, each of which has a differentT-height, the cardinality of this set is at most 1 plus the minimum cardinality of a set that generates the structure.

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