A Functorial Model Theory Newer Applications to Algebraic Topology, Descriptive Sets, and Computing Categories Topos

This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.

IntroductionCategorical PreliminariesCategories and FunctorsMorphismsFunctorsCategorical ProductsNatural TransformationsProducts on Models Preservation of LimitsModel Theory and Topoi More on Universal ConstructionsChapter ExercisesInfinite Language CategoriesBasicsLimits and Infinitary Languages Generic Functors and Language String ModelsFunctorial Morphic Ordered Structure ModelsChapter ExercisesFunctorial Morphic Ordered Structure ModelsFunctorial Fragment Model TheoryIntroductionGeneric Functors and Language String Models Functorial Models As ?-Chains Models Glimpses From Functors Structure Products Higher Stratified Consistency and Completeness Fragment Positive Omitting Type AlgebrasOmitting Types and RealizabilityPositive Categories and Consistency ModelsMore on Fragment ConsistencyChapter ExercisesAlgebraic Theories, Categories, and Models Ultraproducts on AlgebrasUltraproducts and UltrafiltersUltraproduct Applications to Horn Categories Algebraic Theories and Topos Models Free Theories and Factor TheoriesT-Algebras and AdjunctionsTheory Morphisms, Products and Co-products Algebras and the Category of Algebraic TheoriesInitial Algebraic Theories and Computable TreesChapter ExercisesGeneric Functorial Models and ToposElementary TopoiGeneric Functorial ModelsGeneric FunctorsInitial D ModelsPositive Forcing ModelsFunctors Computing Hasse Diagram ModelsFragment Consistent ModelsHomotopy theory of toposFiltered colimits and comma categoriesMore on Yoneda Lemma Chapter ExercisesModels, Sheaves, and ToposPreSheavesDuality, Fragment Models, and TopologyDualityLifts on Topos Models on Cardinalities Chapter ExercisesFunctors on FieldsIntroductionBasic ModelsFieldsPrime Models Omitting Types on FieldsFilters and FieldsFilters and Products Chapter ExercisesFilters and Ultraproducts on Projective SetsGeneral DefinitionsGeneric Functors and Language String Models Functorial Fragment Consistency Filters Structure Products Completing Theories and Fragments Prime Models and Model Completion Uniform and countably incomplete ultrafiltersFunctorial Projetive Set Models and SaturationUltraproducts and Ultrafliters Chapter ExercisesA Glimpse on m Algebraic Set Theory Preliminaries Ultraproducts and Ultrafilters on SetsUltrafilters over N Saturation and PreservationsFunctorial Models and Descriptive Sets Filters, Fragment Constructible Models, and SetsIndex

Dr. Cyrus F. Nourani is a consultant in computing R&D and a research professor at Simon Fraser University. He has many years of experience in the design and implementation of computing systems and has authored/coauthored several books and over 350 publications in mathematics and computer science. He has also held faculty positions at numerous institutions, including the University of Michigan, University of Pennsylvania, University of Auckland, UCLA, and MIT. His research interests include computer science, artificial intelligence, mathematics, virtual haptic computation, information technology, and management.