Introduction To Higher-Order Categorical Logic (Cambridge Studies In Advanced Mathematics)

Author: J. Lambek, P. J. Scott,
Publisher: Cambridge University Press
Keywords: cambridge, studies, advanced, logic, categorical, higher, order, introduction
Pages: 304
Published: 1988-03-25
Language: English
Category: Mathematics, Science,
ISBN-10: 0521356539     ISBN-13: 9780521356534
Binding: Paperback
List Price: 53.00 USD
  • Rating: 80%
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 Detailed historical references are provided throughout, and each section concludeds with a set of exercises.

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