`== Page moved here from ``o-minimality`` ==  I think it's much easier to avoid name clashes by choosing adjective + ``theory`` or adjective + ``structure``, whatever is correct. If both notions exist, I would prefer adjective + ``theory``. If the other notion is really more general, we can split later.  I rescued this from the old talk page:    Hello, I started this article some time ago.  I thought I would outline how I think the page could be productively expanded:  1.  Explain the notion of ``cells`` and why they are nice.  2.  Explain cellular decomposition of definable sets.  3.  Talk about the nice properties of definable families in o-minimal structures.  4.  Explain monotonicity of definable functions.  It may be a concern that some ``supporting notions`` for these ideas have scanty representation on wikipedia as yet, eg the notion of ``definability``. The present article on definability is simply wrong in some respects, and is generally unhelpful.  As much research seems to be happening at present in the theory of weakly o-minimal structures, it might be useful to interleave 1-4 with comments about the analogous results known to hold in the weakly o-minimal case.  Also, it would be nice if there were a page on weak o-minimality.  )  Hunter`