|Date:||Sat, 24 Jan 2009 22:18:03 +0700|
> and yes, category theory relies on logic
called categorical logic perhaps?
4, A little piece of categorical logic
One of the major achievements of category theory in mathematical logic and in computer science, has been a unied treatment of semantics for all kinds of logical systems and term calculi which are the basis for programming languages. One can say that mathematical logic, seen as the study of classical first order logic, rst started to be a real subject with the discovery, by Godel, of the completeness theorem for set-theoretic interpretations: a sentence ' is provable if and only if ' is true in all possible interpretations. This unites the two approaches to logic: proof theory and model theory, makes logic accessible for mathematical methods and enables one to give nice and elegant proofs of proof theoretical properties by model theory (for example, the Beth and Craig denability and interpolation theorems).
Jaap van Oosten
Department of Mathematics
Revised, July 2002
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