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| Paper IPM / M / 17414 | ||||||||||||||||||
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Let M=(M,<,⋯) be a weakly o-minimal structure.
Assume that Def(M) is the collection of all definable sets of M and for any m∈N, Defm(M) is the collection of all definable subsets of Mm in M. We show that the structure M has the strong cell decomposition property if and only if there is an o-minimal structure N such that Def(M)={Y∩Mm: m∈N,Y∈Defm(N)}. Using this result, we prove that:\\
a) Every induced structure has the strong cell decomposition property.\\
b) The structure M has the strong cell decomposition property if and only if the weakly o-minimal structure M∗M has the strong cell decomposition property.\\
Also we examine some properties of non-valuational weakly o-minimal structures in the context of weakly o-minimal structures admitting the strong cell decomposition property.
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