Introduction to Higher-Order Categorical Logic

Cambridge Studies in Advanced Mathematics #7

by J. Lambek, P.J. Scott

In this volume, Lambek and Scott reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher-order logic, and cartesian closed categories, are essentially the same. Part II demonstrates that another formulation of higher-order logic, (intuitionistic) type theories, is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludeds with a set of exercises.

Genres: Logic, Mathematics, Theory

304 pages, Paperback

First published July 25, 1986

Reviews

[D.]

A beautifully clean introduction to the logic of cartesian categories and toposes. With useful "historical perspectives" on the development of the theory.

[Daniel]

post.

Algebraic Type Theory, Part 1: Martin-Löf algebras.