Topoi The Categorial Analysis of Logic

A classic introduction to mathematical logic from the perspective of category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers. Its approach moves always from the particular to the general, following through the steps of the abstraction process until the abstract concept emerges naturally.
Beginning with a survey of set theory and its role in mathematics, the text proceeds to definitions and examples of categories and explains the use of arrows in place of set-membership. The introduction to topos structure covers topos logic, algebra of subobjects, and intuitionism and its logic, advancing to the concept of functors, set concepts and validity, and elementary truth. Explorations of categorial set theory, local truth, and adjointness and quantifiers conclude with a study of logical geometry.

1. Mathematics = Set Theory?
2. What Categories Are
3. Arrows Instead of Epsilon
4. Introducing Topoi
5. Topos Structure: First Steps
6. Logic Classically Conceived
7. Algebra of Subobjects
8. Institutionism and Its Logic
9. Functors
10. Set Concepts and Validity
11. Elementary Truth
12. Categorial Set Theory
13. Arithmetic
14. Local Truth
15. Adjointness and Quantifiers
16. Logical Geometry
References
Catalogue of Notation
Index of Definitions