[FOM] Shipman's field question

[Alasdair Urquhart]

On Wed, 25 Oct 2006, Thomas Forster wrote:

> I recently spent an evening with a friend who had an Executive Toy in the
> form of ball-and-stick gadgets for making toy models of chemicals.  It
> occurred to me that the question of whether or not these structures are
> rigid ( = not deformable) is not obviously trivial.  Is this something on
> which the (decidable) first-order theory of the reals as an ordered field
> has anything amusing to say...?

The right framework for rigidity questions seems to be linear algebra
and its generalizations.  In particular, there is a well developed
theory of combinatorial rigidity in the framework of matroid theory.
As far as I know, Tarski's decision procedure is not useful in this
connection.

Alasdair Urquhart