The geometry of Hrushovski constructions, I. The uncollapsed case

Abstract

An intermediate stage in Hrushovski's construction of flat strongly minimal structures in a relational language L produces omega-stable structures of rank omega. We analyze the pregeometries given by forking on the regular type of rank omega in these structures. We show that varying L can affect the (local) isomorphism type of the pregeometry, but not its finite subpregeometries. A sequel will compare these to the pregeometries of the strongly minimal structures.

arXiv comment31 pages

References in corpus (1)

• The geometry of Hrushovski constructions, II. The strongly minimal case

Cited by in corpus (6)

• Matroid Theory and Hrushovski's Predimension Construction
• Towards a Finer Classification of Strongly Minimal Sets
• The geometry of Hrushovski constructions, II. The strongly minimal case
• The generic flat pregeometry
• An ab initio construction of a geometry
• On reducts of Hrushovski's construction - the non-collapsed case