What is institution-independent model theory
In a broader sense, model theory is the mathematical study of logic language interpretations. In the axiomatic approaches, the concepts and the defining properties are axiomatised rather than considered concretely. Institution-independent model theory is such an axiomatic approach in which all components of logical systems - namely the syntax, the semantics, and the satisfaction relation between them - are treated fully abstractly by relying heavily on category theory. This achieves proper abstraction, relativisation, conceptual clarity, structurally clean causality.
The second edition of the book
After the success of the first edition of this book, published at Birkhauser in 2008, its second edition (which will be soon published by the same publishing house) comes in a heavily reformed form, being re-written from scratch.
There are a lot more supporting explanations. The material - especially the proofs - are strongly structured and outlined, emphasising conceptual and proof milestones. A couple of new chapters on non-classical model theories have been added.
The book is now structured in four parts: basic stuff, advanced (classical) topics, non-classical extensions, and applications to computing science.
There are a lot more supporting explanations. The material - especially the proofs - are strongly structured and outlined, emphasising conceptual and proof milestones. A couple of new chapters on non-classical model theories have been added.
The book is now structured in four parts: basic stuff, advanced (classical) topics, non-classical extensions, and applications to computing science.
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