- 569 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
About this book
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. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.
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Table of contents
- Front Cover
- Topoi: The Categorial Analysis of Logic
- Copyright Page
- Table of Contents
- Dedication
- PREFACE
- PREFACE TO SECOND EDITION
- PROSPECTUS
- CHAPTER 1. MATHEMATICS = SET THEORY?
- CHAPTER 2. WHAT CATEGORIES ARE
- CHAPTER 3. ARROWS INSTEAD OF EPSILON
- CHAPTER 4. INTRODUCING TOPOI
- CHAPTER 5. TOPOS STRUCTURE: FIRST STEPS
- CHAPTER 6. LOGIC CLASSICALLY CONCEIVED
- CHAPTER 7. ALGEBRA OF SUBOBJECTS
- CHAPTER 8. INTUITIONISM AND ITS LOGIC
- CHAPTER 9. FUNCTORS
- CHAPTER 10. SET CONCEPTS AND VALIDITY
- CHAPTER 11. ELEMENTARY TRUTH
- CHAPTER 12. CATEGORIAL SET THEORY
- CHAPTER 13. ARITHMETIC
- CHAPTER 14. LOCAL TRUTH
- CHAPTER 15. ADJOINTNESS AND QUANTIFIERS
- CHAPTER 16. LOGICAL GEOMETRY
- REFERENCES
- CATALOGUE OF NOTATION
- INDEX OF DEFINITIONS
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Yes, you can access Topoi by R. Goldblatt in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over 1.5 million books available in our catalogue for you to explore.