The geometry of Hrushovski constructions, I. The uncollapsed case

Details The geometry of Hrushovski constructions, I. The uncollapsed case The geometry of Hrushovski constructions, I. The uncollapsed case

2011-03-18

arxiv.org/abs/1103.3638v1

Annals of Pure and Applied Logic 162 (2011), pp. 474-488

Mathematics

Logic

31 pages

Scientific paper

10.1016/j.apal.2011.01.008

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.

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