Almost o-minimal structures and \(\mathfrak{X}\)-structures (Q2159928)

The present paper concerns studying new structures introduced by the author: almost o-minimal structures and \(\mathfrak{X}\)-structures. The author proves that an \(\mathfrak{X}\)-expansion of an ordered divisible abelian group always contains an o-minimal expansion of an ordered group where all bounded \(\mathfrak{X}\)-definable sets are definable in the structure. He also proves a uniform local definable cell decomposition theorem for almost o-minimal expansions of ordered groups.