Institution-independent Model Theory

1. Introduction
2. Categories
2.1 Basic Concepts
2.2 Limits and Co-limits
2.3 Adjunctions
2.4 2-categories
2.5 Indexed Categories and Fibrations
3. Institutions
3.1 From concrete logic to Institutions
3.2 Examples of institutions
3.3 Morphisms and Comorphisms
3.4 Institutions as Functors
4. Theories and Models
4.1 Theories and Presentations
4.2 Theory (co-)limits
4.3 Model Amalgamation
4.4 The method of Diagrams
4.5 Inclusion Systems
4.6 Free Models
5. Internal Logic
5.1 Logical Connectives
5.2 Quantifiers
5.3 Substitutions
5.4 Representable Signature Morphisms
5.5 Satisfaction by Injectivity
5.6 Elementary Homomorphisms
6. Model Ultraproducts
6.1 Filtered Products
6.2 Fundamental Theorem
6.3 Los Institutions
6.4 Compactness
6.5 Finitely Sized Models
7. Saturated Models
7.1 Elementary Co-limits
7.2 Existence of Saturated Models
7.3 Uniqueness of Saturated Models
7.4 Saturated Ultraproducts
8. Preservation and Axiomatizability
8.1 Preservation by Saturation
8.2 Axiomatizability by Ultraproducts
8.3 Quasi-varieties and Initial Models
8.4 Quasi-Variety Theorem
8.5 Birkhoff Variety Theorem
8.6 General Birkhoff Axiomatizability
9. Interpolation
9.1 Semantic interpolation
9.2 Interpolation by Axiomatizability
9.3 Interpolation by Consistency
9.4 Craig-Robinson Interpolation
9.5 Borrowing Interpolation
10. Definability
10.1 Explicit implies implicit definability
10.2 Definability by Interpolation
10.3 Definability by Axiomatizability
11. Possible Worlds
11.1 Internal Modal Logic
11.2 Ultraproducts of Kripke models
12. Grothendieck Institutions
12.1 Fibred and Grothendieck Institutions
12.2 Theory Co-limits and Model Amalgamation
12.3 Interpolation
13. Institutions with Proofs
13.1 Free Proof Systems
13.2 Compactness
13.3 Proof-theoretic Internal Logic
13.4 The Entailment Institution
13.5 Birkhoff Completeness
14. Specification
14.1 Structured Specifications
14.2 Specifications with Proofs
14.3 Predefined