Table of Contents:
  • 1. Introduction
  • 2. Basic Notions
  • 2.1. Finiteness Properties
  • 2.2. Rank
  • 2.3. Imaginary Elements
  • 2.4. Orthogonality
  • 2.5. Canonical Projective Geometries
  • 3. Smooth Approximability
  • 3.1. Envelopes
  • 3.2. Homogeneity
  • 3.3. Finite Structures
  • 3.4. Orthogonality Revisited
  • 3.5. Lie Coordinatization
  • 4. Finiteness Theorems
  • 4.1. Geometrical Finiteness
  • 4.2. Sections
  • 4.3. Finite Language
  • 4.4. Quasifinite Axiomatizability
  • 4.5. Ziegler's Finiteness Conjecture
  • 5. Geometric Stability Generalized
  • 5.1. Type amalgamation
  • 5.2. The sizes of envelopes
  • 5.3. Nonmultidimensional Expansions
  • 5.4. Canonical Bases
  • 5.5. Modularity
  • 5.6. Local Characterization of Modularity
  • 5.7. Reducts of Modular Structures
  • 6. Definable Groups
  • 6.1. Generation and Stabilizers
  • 6.2. Modular Groups
  • 6.3. Duality
  • 6.4. Rank and Measure
  • 6.5. The Semi-Dual Cover
  • 6.6. The Finite Basis Property
  • 7. Reducts
  • 7.1. Recognizing Geometries
  • 7.2. Forgetting Constants
  • 7.3. Degenerate Geometries
  • 7.4. Reducts with Groups
  • 7.5. Reducts
  • 8. Effectivity
  • 8.1. The Homogeneous Case
  • 8.2. Effectivity
  • 8.3. Dimension Quantifiers
  • 8.4. Recapitulation and Further Remarks.