Introduction to higher-order categorical logic

✍ Scribed by Lambek J., Scott P.J.

Publisher: Cambridge University Press
Year: 1994
Tongue: English
Leaves: 303
Series: Cambridge Studies in Advanced Mathematics 7
Edition: 4pr.
Category: Library

No coin nor oath required. For personal study only.

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 Detailed historical references are provided throughout, and each section concludeds with a set of exercises

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