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Introduction to higher order categorical…
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Introduction to higher order categorical logic (edition 1986)

by Joachim Lambek, P. J. Scott

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In this book the authors 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. In Part II, it is demonstrated 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 Detailed historical references are provided throughout, and each section concludes with a set of exercises. Thus it is well-suited for graduate courses and research in mathematics and logic. Researchers in theoretical computer science, artificial intelligence and mathematical linguistics will also find this an accessible introduction to a subject of increasing application to these disciplines.… (more)
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Title:Introduction to higher order categorical logic
Authors:Joachim Lambek
Other authors:P. J. Scott
Info:Cambridge [Cambridgeshire] ; New York : Cambridge University Press, c1986.
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Introduction to Higher-Order Categorical Logic by Joachim Lambek

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A beautifully clean introduction to the logic of cartesian categories and toposes. With useful "historical perspectives" on the development of the theory.
  nodier | Dec 19, 2005 |
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Author nameRoleType of authorWork?Status
Lambek, Joachimprimary authorall editionsconfirmed
Scott, P. J.main authorall editionsconfirmed
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