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Weakly o-minimal structure

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A linearly ordered structure, $m$ , with language $L$ including an ordering relation $<$ , is called weakly o-minimal (w.o.-minimal) iff every parametrically definable subset of $m$ is a finite union of convex(definable) subsets. A theory is w.o.-minimal iff all its models are w.o.-minimal.^[1]

^ M.A.Dickmann, Elimination of Quantifiers for Ordered Valuation Rings, The Journal of symbolic Logic, Vol. 52, No. 1 (Mar., 1987), pp 116-128. [[1]]

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