Some definable properties of sets in non-valuational weakly o-minimal structures
The author studies properties of non-valuational weakly o-minimal expansions of real closed fields and ordered groups. He proves that every non-valuational weakly o-minimal expansion of a real closed field has a \(C^r\)-strong cell decomposition property for each positive integer \(r\). The author also proves that the curve selection property holds in non-valuational weakly o-minimal expansions of ordered groups. At last, he presents a criterion for definable compactness of a definable set in a non-valuational weakly o-minimal expansion of an ordered group.
non-valuational weakly o-minimal expansions of real closed fields and ordered groups
a \(C^r\)-strong cell decomposition property
scientific article; zbMATH DE number 6714186