Topoi: Categorial Analysis of Logic (Studies in Logic and the Foundations of Mathematics) - Hardcover

Goldblatt, Robert

Hardcover

ISBN 10: 0444852077 ISBN 13: 9780444852076

Publisher: Elsevier Science Ltd, 1979

Synopsis

The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''. The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes.

About this edition

• Publisher: Elsevier Science Ltd
• Publication date: 1979
• ISBN 10: 0444852077
• ISBN 13: 9780444852076
• Binding: Hardcover
• Number of pages: 502