http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Algebraic computability and enumeration models
recursion theory and descriptive complexity
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 descri.
1. Introduction -- 2. Computing categories, language fragments, and models -- 3. Functorial admissible models -- 4. Initial tree computing and languages -- 5. Descriptive sets and infinitary languages -- 6. Complexity and computing -- 7. Arithmetic hierarchy and enumeration degrees -- 8. Peano arithmetic models and computability -- 9. Realizability and computability.
Includes bibliographical references and index.