2004/06/26 by Tristram de Piro, de Piro, Tristram
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.math/0406543
arxiv created 2004/06/26 · openalex publication_date 2004/06/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with extending results from "The Geometry of 1-Based Minimal Types" by Kim and the present author. We work in the more general context of the solution set D of a regular Lascar Strong Type defined over the empty set in a simple theory T. In Pillay's book "Geometric Stability Theory", a notion of p-weight is developed for regular types in stable theories. Here we show that the corresponding notion holds in simple theories and give a geometric analysis of associated structures G(D) and G(D)(large), the former of which appears in the above paper. We show that D is linear iff G(D) and G(D)(large) (localized, respectively) are both modular with respect to the p-closure operator. Finally, we show that modularity of G(D)(large) provides a local analogue of 1-basedness for the theory T.