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.

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...

Ecosystems and Technology: Idea Generation and Content Model Processing, presents important new innovations in the area of management and computing. Innovation is the generation and application of new ideas and skills to produce new products, processes, and services that improve economic and social prosperity. This includes management and design policy decisions and encompasses innovation research, analysis, and best practice in enterprises, public and private sector service organizations, government, regional societies and economies.

The book, the first volume in...