Weakly o-minimal structure

Weakly o-minimal structure

= Weakly O-Minimal Definition =

A linearly ordered structure, m, with language L including anordering relation <, is called "weakly o-minimal (w.o.-minimal)" iffevery 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.

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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