During this quantity, Lambek and Scott reconcile diversified viewpoints of the principles of arithmetic, particularly mathematical common sense and classification idea. partially I, they exhibit that typed lambda-calculi, a formula of higher-order common sense, and cartesian closed different types, are basically a similar. half II demonstrates that one other formula of higher-order good judgment, (intuitionistic) variety theories, is heavily relating to topos concept. half III is dedicated to recursive services. quite a few purposes of the shut courting among conventional common sense and the algebraic language of classification idea are given. The authors have incorporated an advent to classification idea and advance the required common sense as required, making the booklet basically self-contained. unique old references are supplied all through, and every part concludeds with a collection of workouts.

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