Introduction to Higher-Order Categorical Logic

✍ Scribed by J. Lambek, P. J. Scott

Publisher: Cambridge University Press
Year: 1988
Tongue: English
Leaves: 301
Series: Cambridge Studies in Advanced Mathematics 7
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

I was looking for a book for my girlfriend this Christmas and stumbled upon this one. At first I thought it would be too light but was I ever mistaken!! This book is so high that it would make Jack Kerouac dizzy. It begins with a treatment of basic category theory and ccc's and then goes on to present toposes and intuitionistic type theory. The authors take care to annotate their turnstile with the set of free variables (Hah! I bet you thought I had no idea what this book was about!) so that they can deal with empty types in a reasonable way. The treatment of presheaf models is very lucid and the discussion of internal languages and lambda-calculi is excellent. In fact many papers of Koymans are just exercises from this book worked out. The book is slightly out of date, no treatment of linear logic or symmetric monoidal-closed categories. Overall this book is highly recommended for the beginner and expert alike.

📜 SIMILAR VOLUMES

Introduction to Higher-Order Categorical

📁 Introduction to Higher-Order Categorical Logic

✍ J. Lambek, P.J. Scott 📂 Library 📅 1986 🏛 Cambridge University Press 🌐 English

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

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Introduction to Higher Order Categorical

📁 Introduction to Higher Order Categorical Logic

✍ J. Lambek, P. J. Scott 📂 Library 📅 1988 🏛 Cambridge University Press 🌐 English

Introduction to Higher-Order Categorical

📁 Introduction to Higher-Order Categorical Logic

✍ J. Lambek, P. J. Scott 📂 Library 📅 1988 🏛 Cambridge University Press 🌐 English

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.

Introduction to higher-order categorical

📁 Introduction to higher-order categorical logic

✍ J. Lambek, P. J. Scott 📂 Library 📅 1988 🏛 Cambridge University Press 🌐 English