[FOM] FOM: Pointless Geometry

[A. Mani]

On Saturday 26 November 2005 08:19, John Corcoran wrote:
> Article II "Foundations of the Geometry of Solids" of Tarski's LOGIC,
> SEMANTICS, METAMATHEMATICS understands by "a geometry of solids"  the
> following: "a system of geometry destitute of such geometrical figures
> as points, lines, and surfaces, and admitting as figures only solids
> ...".
> Tarski, A., LOGIC, SEMANTICS, METAMATHEMATICS revised edition with new
> introduction by J. Corcoran, Hackett Publishing Company, Indianapolis
> (1983) Originally published by Oxford: Oxford University Press, 1956.
> MR85e:01065.
The original Tarski paper dates to 1929. It is based on Lesniewski's 
mereology. The models are isomorphic to regular open sets of usual euclidean 
geometry. 

I found this paper,
Bennet, B et al "Region Based Qualitative Geometry"
http://citeseer.ist.psu.edu/bennett00regionbased.html

The authors deal with it and proceed to form a slightly modified axiomatic 
system. 


A. Mani
Member, Cal. Math. Soc