We prove that if ℳ = (M,≤,+,...) is a weakly o-minimal non-valuational structure expanding an ordered group (M,≤,+), then its expansion by a family of "non-valuational" unary predicates remains non-valuational. The paper is based on the author's earlier work on strong cell decomposition for weakly o-minimal non-valuational expansions of ordered groups.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm202-2-3, author = {Roman Wencel}, title = {On expansions of weakly o-minimal non-valuational structures by convex predicates}, journal = {Fundamenta Mathematicae}, volume = {205}, year = {2009}, pages = {147-159}, zbl = {1159.03024}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm202-2-3} }
Roman Wencel. On expansions of weakly o-minimal non-valuational structures by convex predicates. Fundamenta Mathematicae, Tome 205 (2009) pp. 147-159. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm202-2-3/