Opis: Algebraic Computability and Enumeration Models - Cyrus Nourani

This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic types of models. New homotopy techniques are applied to Marin Lof types of computations with model categories. Functorial computability, induction, and recursion are examined in view of the above, presenting new computability techniques with monad transformations and projective sets. This informative volume will give readers a complete new feel for models, computability, recursion sets, complexity, and realizability. This book pulls together functorial thoughts, models, computability, sets, recursion, arithmetic hierarchy, filters, with real tree computing areas, presented in a very intuitive manner for university teaching, with exercises for every chapter. The book will also prove valuable for faculty in computer science and mathematics.Preface Introduction Computing Categories, Language Fragments, and Models Introduction Limits and Infinitary Languages Generic Functors and Language String Models Positive Generic Models Fragment Consistent Algebras Generic Products Positive Morphisms and Models Positive Consistency and Omitting Types Positive Fragment Consistency Models Horn Models Positive Categories and Horn Fragments Fragment Consistent Kleene Models More on Kleene Structures Process Algebras Functorial Admissible Models Infinitary Languages Basics Admissible Languages Admissible Models Infinite Language Categories A Descriptive Computing Computing Model Diagrams Situations and Compatibility Boolean Computing Diagrams Description Logic Functorial Model Theory and HIFI Computing Generic Functor Initial Models Initial Tree Algebras and Amplification Tree Amplifiers and The Sonic Booms The Recursion Theorem Tree Amplifiers and Recursion Admissible Gain Synthesizer Initial Tree Computing and Languages Initial Models and Their Algebraic Formulation The Basics Canonical Models Generic diagrams of Initial Models Initial Algebras and Computable Trees Tree Rewriting, Algebras, and Infinitary Models Are There Models for Nothing Free Proof Trees and Computing Models Generating Models by Positive Forcing Algebraically Closed Groups Word Problems and the SRS Roller Coaster The Roller Coaster Private Languages and Wittgenstein's Paradox Concluding Comments Descriptive Sets and Infinitary Languages Introduction Admissible Sets and Structures Basic Descriptive Characterizations Boolean Valued Models Admissible Sets and Ordinals Error! Bookmark not defined. Set Reducibility Admissible Tree Recursion Admissible Set Reducibility Complexity and Computing Introduction Forcing, Complexity, and Diaphontine Definability Technical Preliminaries Initial Models Generic Diagrams for Initial Models Models and Fragment Inductive Closure Positive Forcing and Infinitary Models Generating Models by Positive Forcing Forcing and Computability Complexity Classes, Models, and Urlements Functorial Implicit Complexity Error! Bookmark not defined. Abstract Descriptive Complexity A Descriptive Computing Example Revisit Rudiments, KPU, and Recursion Admissible Hulls Concrete Descriptive Complexity Concrete Implicit Complexity Overview to Arithmetic Hierarchy Arithmetic Hierarchy and Enumeration Degrees Introduction Turing Degrees and Isomorphism Types Arithmetic Hierarchy and Infinitary Languages Computability and Hierarchy with Infinitary Languages Computability on Infinitary Languages Enumeration Degrees Enumeration Definability and Turing Jumps Automorphisms and Lifts on K-Pairs Enumeration Computability Models Rudiments, KPU, and Recursion Computable Categorical Trees Enumerations Model Theory Peano Arithmetic Models and Computability Introduction Recursion on Arithmetic Fragments Godel's Incompleteness and Ordinal Arithmetic Descriptive Sets and Automata Finite Models Fields and Fragments of Peano Arithmetic Arithmetic Hierarchy and Borel Sets Infinitary Theories and c=Countable N Models KPU Ordinal Models Generic Computability and Filters Realizability and Computability Introduction Categorical Models and Realizability Categorical Intuitionistic Models Infinitary Language Product Models Positive Generic Models Omitting Types Realizability Positive Realizability Morphisms and Models Fragment Product Algebra Realizability Positive Realizability on Horn Filters Computability and Positive Realizability Morphic Realization Functors Positive Categories and Consistency Models Horn Computability and Realizability Intuitionistic Types and Realizability Realizability on Ultrafilters Computing Morphisms on Topos Relative Realizability on Topos Realizability Triposes More on Topos Realizability On PreSheaves Topos Realizability Index

Szczegóły: Algebraic Computability and Enumeration Models - Cyrus Nourani

Tytuł: Algebraic Computability and Enumeration Models
Autor: Cyrus Nourani
Wydawnictwo: Apple
ISBN: 9781771882477
Rok wydania: 2016
Ilość stron: 310
Oprawa: Twarda
Waga: 0.57 kg

Recenzje: Algebraic Computability and Enumeration Models - Cyrus Nourani