Introduction to Higher-Order Categorical Logic (Cambridge Studies in Advanced Mathematics, Series Number 7) by J. Lambek (PDF)

Description

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 Detailed historical references are provided throughout, and each section concludeds with a set of exercises.

User’s Reviews

Editorial Reviews: Review “…important monograph…very clearly written…” SciTech Book News”…a readable and timely account of important results, most of which were not previously available in book form.” London Mathematical Society”[The authors] present their material as persuasively and as lucidly as possible. In addition, they have included many useful exercises and illuminating historical and philosophical remarks, which should make the book attractive to an audience not confined to the already expert. This is an excellent and timely work on a subject that is assuming an increasingly important role in the foundations of mathematics.” J.L. Bell, Journal of Symbolic Logic

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This text offers valuable insights for many a logician, from the standpoint of computing and mathematics.It is less useful from a philosophical viewpoint, as many of the contents relate directly to mathematics and not philosophy.It’s an interesting case: I don’t exactly recommend this book, even though the writing is of very high quality.

⭐

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