Is there a model theory textbook that describes how to build boolean-valued models to prove the consistency of a sentence with a theory? It would be great if the book also contained basic techniques to prove the independence of a sentence from a given set of sentences. P.S. I'm a beginner and looking for a rather clear and not encyclopedic book. I already have Keisler's, Tent's and Hodges' electronic books but don't know if they are good to study the topics I've mentioned.
2026-03-29 20:04:33.1774814673
Model theory textbook to learn about the consistency and independency proofs
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You will not find Boolean-valued models in any model theory textbooks. Instead, you want a set theory book that takes the Boolean-values models approach to forcing.
The classic is Bell's Set Theory: Boolean-Valued Models and Independence Proofs.
Another option is Jech's Set Theory, but this book is definitely encyclopedic!