Topoi The Categorial Analysis of Logic

Name: Topoi The Categorial Analysis of Logic
Price: 15.71 USD
Availability: InStock
ISBN: 9780486450261

ISBN-10: 0486450260

ISBN-13: 9780486450261

Edition: 2006

Authors: Robert Goldblatt

List price: $32.95

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Description:

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.

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


Preface to Second Edition


Preface to Dover Edition


Prospectus



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



Duality



Products



Co-products



Equalisers



Limits and co-limits



Co-equalisers



The pullback



Pushouts



Completeness



Exponentiation



Introducing Topoi



Subobjects



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



[epsilon]-semantics



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



Functors



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



Validity



Applications



Elementary Truth



The idea of a first-order language



Formal language and semantics



Axiomatics



Models in a topos



Substitution and soundness



Kripke models



Completeness



Existence and free logic



Heyting-valued sets



High-order logic



Categorial Set Theory



Axioms of choice



Natural numbers objects



Formal set theory



Transitive sets



Set-objects



Equivalence of models



Arithmetic



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



Adjunctions



Some adjoint situations



The fundamental theorem



Quantifiers



Logical Geometry



Preservation and reflection



Geometric morphisms



Internal logic



Geometric logic



Theories as sites


References


Catalogue of Notation


Index of Definitions