The geometry of Hrushovski constructions, I: The uncollapsed case

David M. Evans; Marco S. Ferreira

doi:10.1016/j.apal.2011.01.008

The geometry of Hrushovski constructions, I: The uncollapsed case

David M. Evans
, Marco S. Ferreira

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

An intermediate stage in Hrushovski’s construction of flat strongly minimal structures in a relational language L produces ?-stable structures of rank ?. We analyze the pregeometries given by forking on the regular type of rank ? 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.

Original language	English
Pages (from-to)	474-488
Number of pages	15
Journal	Annals of Pure and Applied Logic
Volume	162
Issue number	6
DOIs	https://doi.org/10.1016/j.apal.2011.01.008
Publication status	Published - Apr 2011

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10.1016/j.apal.2011.01.008Licence: Other

Cite this

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title = "The geometry of Hrushovski constructions, I: The uncollapsed case",

abstract = "An intermediate stage in Hrushovski{\textquoteright}s construction of flat strongly minimal structures in a relational language L produces ?-stable structures of rank ?. We analyze the pregeometries given by forking on the regular type of rank ? 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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AB - An intermediate stage in Hrushovski’s construction of flat strongly minimal structures in a relational language L produces ?-stable structures of rank ?. We analyze the pregeometries given by forking on the regular type of rank ? 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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