Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity

Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity

by Cyrus F. Nourani

Hardcover

$190.00
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Product Details

ISBN-13: 9781771882477
Publisher: Apple Academic Press
Publication date: 02/24/2016
Pages: 310
Product dimensions: 6.00(w) x 9.00(h) x 0.90(d)

About the Author

Dr. Cyrus F. Nourani has a national and international reputation in computer science, artificial intelligence, mathematics, virtual haptic computation, information technology, and management. He has many years of experience in the design and implementation of computing systems. Dr. Nourani's academic experience includes faculty positions at the University of Michigan-Ann Arbor, the University of Pennsylvania, the University of Southern California, UCLA, MIT, and the University of California, Santa Barbara. He was also research professor at Simon Frasier University in Burnaby, British Columbia, Canada. He was a visiting professor at Edith Cowan University, Perth, Australia, and a lecturer of management science and IT at the University of Auckland, New Zealand.

Dr. Nourani commenced his university degrees at MIT where he became interested in algebraic semantics. That was pursued with a category theorist at the University of California. Dr. Nourani’s dissertation on computing models and categories proved to have intuitionist forcing developments that were published from his postdoctoral times on at ASL. He has taught AI to the Los Angeles aerospace industry and has authored many R&D and commercial ventures. He has written and co-authored several books. He has over 350 publications in mathematics and computer science and has written on additional topics, such as pure mathematics, AI, EC, and IT management science, decision trees, predictive economics game modeling. In 1987, he founded Ventures for computing R&D. He began independent consulting with clients such as System Development Corporation (SDC), the US Air Force Space Division, and GE Aerospace. Dr. Nourani has designed and developed AI robot planning and reasoning systems at Northrop Research and Technology Center, Palos Verdes, California. He also has comparable AI, software, and computing foundations and R&D experience at GTE Research Labs.

Table of Contents

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

Customer Reviews

Most Helpful Customer Reviews

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