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Müller, Isabel: An ample geometry of finite rank. 2017
Content
Introduction
Preliminaries
Some Model Theory
Around Zil'ber's Conjecture
Incidence Geometries
The Construction
Motivation and Notation
The Predimension Function
The Amalgamation Class
Around Submodularity
Dimension and Minimal Extensions
Amalgamation
The ab-initio structure
Axiomatization
Forking
Ranks
Ampleness
The Finite-Rank Geometry
The Collapse
Geometrical Properties of M
Saturation
Rank and Ampleness
Coordinatisation
Description of Forking
The Rank
Ampleness
A new Counterexample
Groups in Pregeometries
The Group Configuration Theorem
Trivial Forking
Flat Geometries
Groups in M
Bounded Automorphisms
Lascar's Result
In Generalized N-Gons
In the 2-Ample Geometry
New Simple Groups
Epilogue