Categorical Models of Constructive Logic
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author = {Thomas Streicher Fachbereich and Thomas Streicher and Fachbereich Mathematik and Tu Darmstadt},
title = {Categorical Models of Constructive Logic},
year = {}
}
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Abstract:
Introduction If asked why one should be interested in constructive (intuitionistic) logic besides saying that it is a nice subject that makes a lot of fun I could give the following two more serious reasons (1) from proofs in constructive logic one may extract algorithms, bounds etc. (2) weakening the logic allows one to postulate axioms that are classically false, e.g. all functions are computable or all functions are continuous. The issues raised in (1) are typically dealt with by proof theory whereas those raised in (2) are best treated via the methods of Categorical Logic and that's what these lectures are about: in other words the model theory of constructive logic. However, its avour will be very dierent from classical model theory. The essential dierence is that for the purposes of constructive logic we can not restrict ourselves to 2-valued models (as 2-valued models automatically validate the priciple of excluded middle). Notice that even for classical logic and set th
Citations
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