High Quality Content by WIKIPEDIA articles! In mathematics, specifically the field of model theory, a weakly o-minimal structure is a model theoretic structure whose definable sets in the domain are just finite unions of convex sets. A linearly ordered structure, M, with language L including an ordering relation , is called weakly o-minimal if every parametrically definable subset of M is a finite union of convex (definable) subsets. A theory is weakly o-minimal if all its models are weakly o-minimal. Note that, in contrast to o-minimality, it is possible for a theory to have models which are weakly o-minimal and to have other models which are not weakly o-minimal.