Weakly o-minimal structure
- Weakly o-minimal structure
= Weakly O-Minimal Definition =
A linearly ordered structure, , with language including anordering relation , is called "weakly o-minimal (w.o.-minimal)" iffevery parametrically definable subset of is a finite union of convex (definable) subsets.A theory is "w.o.-minimal" iff all its models are w.o.-minimal.
Note that, in contrast to o-minimality, it is possible for a theory to have models which are w.o.-minimal and to have other models which are not w.o.-minimal.
[M.A.Dickmann, "Elimination of Quantifiers for Ordered Valuation Rings", The Journal of symbolic Logic, Vol. 52, No. 1 (Mar., 1987), pp 116-128. [http://www.jstor.org/view/00224812/di985230/98p04615/0] ]
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