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Many sorted languages are the natural way how to formalize mathematical theories. This text provides an introduction to many-sorted logic and models. Our main focus is to formulate and prove the most important theorems of mathematical logic: The Correctness, Completeness and Compactness Theorems. We will also present examples of common many-sorted languages along the way, including the language of modules over rings, of ring-extensions and that of sets and classes.Contents:1. What do we have here?2. Defining Many-Sorted Languages3. Examples of Many-Sorted Languages4. Formal Deduction5. First Results6. Defining Many-Sorted Models7. The Theory of Proofs8. Henkin's Theory
source https://www.free-ebooks.net/mathematics-textbooks/Many-Sorted-Logic
