Categorical Abstract Algebraic Logic:
Hierarchies of π-Institutions^®

© George Voutsadakis

These notes may eventually take the shape of an Online Monograph on Categorical Abstract Algebraic Logic.

• They include already established definitions and previously obtained results, modifications reflecting my current understanding and viewpoint, corrections of errors that I have regrettably made in previous works, but also ongoing research.
  
• Remarks, suggestions and notifications of errors are welcome.
• Help with OPEN PROBLEMS and with missing EXAMPLES & COUNTEREXAMPLES is also welcome.
• To refer to a result found in these notes (or, for that matter, to the work as a whole), please use:
• Voutsadakis, G., Categorical Abstract Algebraic Logic: Hierarchies of π-Institutions, Online Monograph in progress available at http://www.voutsadakis.com/RESEARCH/caal.html
But be aware that, being in flux, the numbering will be constantly changing (and the general structure may also change).

Version 0.97 (March 2023)

0. Cover and Table of Contents (in progress)
1. Introduction (in progress)
   
2. Algebra and Logic (in progress)
   
3. The Semantic Leibniz Hierarchy: Bottom Half (in progress)
4. The Semantic Leibniz Hierarchy: Top Half (in progress)
5. The Semantic Leibniz Hierarchy: Extensionality (in progress)
   
6. The Semantic Leibniz Hierarchy: Under the Bottom I (in progress)
7. The Semantic Leibniz Hierarchy: Under the Bottom II (in progress)
   
8. The Semantic Leibniz Hierarchy: Over the Top I (in progress)
   
9. The Semantic Leibniz Hierarchy: Over the Top II (in progress)
   
10. Elements of Syntax (in progress)
    
11. The Syntactic Leibniz Hierarchy: Foundations (in progress)
    
12. The Syntactic Leibniz Hierarchy: Edifice (in progress)
13. The Syntactic Leibniz Hierarchy: Parameterlessness (in progress)
    
14. The Syntactic Leibniz Hierarchy: Basement I (in progress)
15. The Syntactic Leibniz Hierarchy: Basement II (in progress)
    
16. The Syntactic Leibniz Hierarchy: Attic I (in progress)
    
17. The Syntactic Leibniz Hierarchy: Attic II (in progress)
    
18. Properties of Selected Classes (in progress)
19. Full Models of π-Institutions (in progress)
    
20. Full Adequacy (in progress)
    
21. Operators on π-Institutions (in progress)
    
22. The Strong Version of a π-Institution (in progress)
    
23. The Frege Hierarchy (in progress)
    
24. Special Topics (in progress)
25. Order Algebraizability (in progress)
26. Gentzen π-Institutions (in progress)
    
27. Behavioral Algebraizability (in progress)
28. List of Problems (in progress)
    
29. Bibliography (in progress)
    
30. Index of Terms (in progress)
    
31. Index of Symbols (in progress)
32. Index of Classes (in progress)