[FOM] FOM: Pointless Geometry
A. Mani
a_mani_sc_gs at yahoo.co.in
Sun Nov 27 20:04:23 EST 2005
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
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