Pregeometry

From Wikipedia, the free encyclopedia

Pregeometry, and in full combinatorial pregeometry, are obsolescent names for a matroid, introduced by G.-C. Rota with the intention of providing a less "ineffably cacaphonous" alternative term. Also, the term combinatorial geometry, sometimes abbreviated to geometry, was intended to replace simple matroid. These terms are now infrequently used in the study of matroids.

In the branch of mathematical logic called model theory, however, these terms are universally used in the discussion of independence phenomena (essentially as defined by Rota.) The study of how pregeometries, geometries, and abstract closure operations influence the structure of first-order models is called geometric stability theory.

[edit] Reference

H.H. Crapo and G.-C. Rota (1970). On the Foundations of Combinatorial Theory: Combinatorial Geometries. M.I.T. Press, Cambridge, Mass.

Pillay, Anand (1996). "Geometric Stability Theory (Oxford Logic Guides)" Oxford University Press, USA