Cardinality of the sets of dimension functions in ordered structures
Authors
Masato Fujita
Abstract
We compute the cardinality of the sets of dimension functions on the ordered structures . The inequality holds if is a d-minimal expansion of an ordered group. If is o-minimal and , there exists a positive integer such that . For every positive integer , there exists a weakly o-minimal expansion of an ordered divisible Abelian group such that .
