# Model Theory

**Type:** Concept  
**Domain:** foundations-logic  
**Codex URL:** /mathematics/foundations-logic/model-theory/  
**Entry status:** Live — v1.0 (2026-07-09)

## Summary
Studies the relationship between formal languages and the structures (models) that satisfy them. Löwenheim-Skolem, compactness, Morley categoricity theorem, Shelah's stability theory, o-minimality, applications to algebra.

## Sources
- [Tier 1] Marker, D. (2002). Model Theory: An Introduction. Springer.
- [Tier 1] Shelah, S. (1990). Classification Theory. Revised ed.
- [Tier 2] Hodges, W. (1993). Model Theory. Cambridge University Press.
- [Tier 3] Chang, C.C. and Keisler, H.J. (1990). Model Theory. 3rd ed.

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*Mathematics Codex entry v1.0 — added 2026-07-09 — thecodex.expert/mathematics/*