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Topoi The Categorial Analysis of Logic

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ISBN-10: 0486450260

ISBN-13: 9780486450261

Edition: 2006

Authors: Robert Goldblatt

List price: $32.95
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A classic exposition of a branch of mathematical logic that uses category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers. Robert Goldblatt is Professor of Pure Mathematics at New Zealand's Victoria University. 1983 edition.
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Book details

List price: $32.95
Copyright year: 2006
Publisher: Dover Publications, Incorporated
Publication date: 4/28/2006
Binding: Paperback
Pages: 576
Size: 5.47" wide x 8.46" long x 1.14" tall
Weight: 1.562
Language: English

Preface to Second Edition
Preface to Dover Edition
Mathematics = Set Theory?
Set theory
Foundations of mathematics
Mathematics as set theory
What Categories Are
Functions are sets?
Composition of functions
Categories: first examples
The pathology of abstraction
Basic examples
Arrows Instead of Epsilon
Monic arrows
Epic arrows
Iso arrows
Isomorphic objects
Initial objects
Terminal objects
Limits and co-limits
The pullback
Introducing Topoi
Classifying subobjects
Definition of topos
First examples
Bundles and sheaves
Monoid actions
Power objects
[Omega] and comprehension
Topos Structure: First Steps
Monics equalise
Images of arrows
Fundamental facts
Extensionality and bivalence
Monics and epics by elements
Logic Classically Conceived
Motivating topos logic
Propositions and truth-values
The propositional calculus
Boolean algebra
Algebraic semantics
Truth-functions as arrows
Algebra of Subobjects
Complement, intersection, union
Sub(d) as a lattice
Boolean topoi
Internal vs. external
Implication and its implications
Filling two gaps
Extensionality revisited
Intuitionism and its Logic
Constructivist philosophy
Heyting's calculus
Heyting algebras
Kripke semantics
The concept of functor
Natural transformations
Functor categories
Set Concepts and Validity
Set concepts
Heyting algebras in P
The subobject classifier in Set[superscript p]
The truth arrows
Elementary Truth
The idea of a first-order language
Formal language and semantics
Models in a topos
Substitution and soundness
Kripke models
Existence and free logic
Heyting-valued sets
High-order logic
Categorial Set Theory
Axioms of choice
Natural numbers objects
Formal set theory
Transitive sets
Equivalence of models
Topoi as foundations
Primitive recursion
Peano postulates
Local Truth
Stacks and sheaves
Classifying stacks and sheaves
Grothendieck topoi
Elementary sites
Geometric modality
Kripke-Joyal semantics
Sheaves as complete [Omega]-sets
Number systems as sheaves
Adjointness and Quantifiers
Some adjoint situations
The fundamental theorem
Logical Geometry
Preservation and reflection
Geometric morphisms
Internal logic
Geometric logic
Theories as sites
Catalogue of Notation
Index of Definitions