Introduction to Higher-Order Categorical Logic (Cambridge Studies in Advanced Mathematics, Series Number 7)

Lambek, J.; Scott, P. J.

ISBN 10: 0521356539 / ISBN 13: 9780521356534

Published by Cambridge University Press, 1988

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Synopsis:

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 Detailed historical references are provided throughout, and each section concludeds with a set of exercises.

Book Description: Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

Bibliographic Details

Title: Introduction to Higher-Order Categorical ...
Publisher: Cambridge University Press
Publication Date: 1988
Binding: Soft cover
Condition: New