Topoi: The Categorial Analysis of Logic (Volume 98) (Studies in Logic and the Foundations of Mathematics, Volume 98) - Hardcover

Goldblatt, R.

Hardcover

ISBN 10: 0444867112 ISBN 13: 9780444867117

Publisher: North Holland, 1984

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.

Edition details

• Publisher: North Holland
• Publication date: 1984
• ISBN 10: 0444867112
• ISBN 13: 9780444867117
• Binding: Hardcover
• Language: English
• Edition number: 2
• Number of pages: 565