# nLab logical scheme

model theory

## Dimension, ranks, forking

• forking and dividing?

• Morley rank?

• Shelah 2-rank?

• Lascar U-rank?

• Vapnik–Chervonenkis dimension?

# Contents

### Idea

Logical schemes are geometric entities which relate to first-order logical theories in much the same way that algebraic schemes relate to commutative rings. They are used to establish a categorification of Stone duality relating first-order theories and their categories of models. This is an alternative to the approach via ultracategories. In this framework conceptual completeness can be established.