On lovely pairs of geometric structures

Annals of Pure and Applied Logic 161 (7):866-878 (2010)
Abstract
We study the theory of lovely pairs of geometric structures, in particular o-minimal structures. We use the pairs to isolate a class of geometric structures called weakly locally modular which generalizes the class of linear structures in the settings of SU-rank one theories and o-minimal theories. For o-minimal theories, we use the Peterzil–Starchenko trichotomy theorem to characterize for a sufficiently general point, the local geometry around it in terms of the thorn U-rank of its type inside a lovely pair
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DOI 10.1016/j.apal.2009.10.004
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References found in this work BETA
Generic Structures and Simple Theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
Lovely Pairs of Models.Itay Ben-Yaacov, Anand Pillay & Evgueni Vassiliev - 2003 - Annals of Pure and Applied Logic 122 (1-3):235-261.
Pseudoprojective Strongly Minimal Sets Are Locally Projective.Steven Buechler - 1991 - Journal of Symbolic Logic 56 (4):1184-1194.
Properties and Consequences of Thorn-Independence.Alf Onshuus - 2006 - Journal of Symbolic Logic 71 (1):1 - 21.
Generic Pairs of SU-Rank 1 Structures.Evgueni Vassiliev - 2003 - Annals of Pure and Applied Logic 120 (1-3):103-149.

View all 12 references / Add more references

Citations of this work BETA
Weakly One-Based Geometric Theories.Alexander Berenstein & Evgueni Vassiliev - 2012 - Journal of Symbolic Logic 77 (2):392-422.
Dimensions, Matroids, and Dense Pairs of First-Order Structures.Antongiulio Fornasiero - 2011 - Annals of Pure and Applied Logic 162 (7):514-543.
Generic Trivializations of Geometric Theories.Alexander Berenstein & Evgueni Vassiliev - 2014 - Mathematical Logic Quarterly 60 (4-5):289-303.

View all 9 citations / Add more citations

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