Talk:O-minimality

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

Example
Hi, I removed the following from the examples:


 * 1) Any model of the axioms for a linear order in the language L = {<}.

Reason: Consider Q concatonated with a copy of Z. i.e. for each q \in Q and z \in Z put q<z. This is a linear order, but the set of elements with a succsesor is definable, and is Z. This has no infimum. Thehalfone 12:58, 11 June 2007 (UTC)


 * I would guess the original author intended to say "dense linear order"; consider fixing things like that rather than removing them entirely. &mdash; Carl (CBM · talk) 20:57, 11 June 2007 (UTC)


 * Point taken! Thehalfone 10:26, 12 June 2007 (UTC)