Weakly o-minimal structure
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[edit] Weakly O-Minimal Definition
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.
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.
