nLab model theory - contents

model theory

Basic concepts and techniques

• language, signature

• theory, first-order theory

• model

• interpretation

• structure in model theory

• elementary embedding

• type in model theory

• compactness theorem

• diagram of a first-order structure

• definable set

• (combinatorial) pregeometry

• ultraproduct, ultraroot, ultrapower

• indiscernible sequence?

• Morleyization

• Morley sequence?

• Ramsey theorem?

• Erdos-Rado theorem?

• Ehrenfeucht-Fraïssé games (back-and-forth games)

Dimension, ranks, forking

• forking and dividing?

• Morley rank?

• Shelah 2-rank?

• Lascar U-rank?

• Vapnik–Chervonenkis dimension?

Universal constructions

• Fraïssé limits

• monster model

• Hrushovski construction?

• product of theories

Extra stuff, structure, properties

• definable group

• definable groupoid

• definable category

• elimination of imaginaries

• elimination of hyperimaginaries

• elimination of quantifiers

• omega-categorical structure

• existentially closed model

• model completeness

• stable theories

• geometric stability theory

• generic predicate?

• ultracategory

Examples

• ACF

• DLO

• countable random graph

• ACVF?

• RCF?

• nonstandard analysis

• Peano arithmetic

• Robinson arithmetic

• Nelson arithmetic

Theorems

• Ax-Kochen-Ershov theorem?

• Keisler-Shelah isomorphism theorem

• conceptual completeness

• Makkai duality

• Los ultraproduct theorem

• Morley categoricity theorem?

• omitting types theorem

• Deligne completeness theorem