Talk:O-minimal theory

From Wikipedia, the free encyclopedia

[edit] 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. --Hans Adler (talk) 19:09, 23 November 2007 (UTC)

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