Intends to lay a common basis for the different branches of
recursion theory. Leads from the very basic theory to modern
concepts of computability. Consists of three consecutiveparts: 1. Basic Concepts of Computability. 2. Traditional
Recursion Theory. 3. Unified Type 2 theory of constructivity
and computability on Baire's space including a general the-
ory of representations.

Autorentext
Klaus Weihrauch ist seit 1990 bei der SAP AG und dort im Umfeld der Lösung Produktionsplanung und -steuerung (PP) tätig. Unter anderem erstellte er das Daten- und Prozessmodell für die R/3-Komponente PP und war im Rahmen von AcceleratedSAP für den Bereich der Produktionsplanung verantwortlich. Zurzeit ist Klaus Weihrauch Projektleiter im Bereich Best Practices for mySAP SCM, in dem vorkonfigurierte Lösungen für das Supply Chain Management erstellt werden.

Inhalt
Prerequisites and Notation.- 1: Basic Concepts of Computability.- 1.1 Flowcharts and Machines.- 1.2 Register Machines and Register Computability.- 1.3 Primitive Recursive and ?-Recursive Functions.- 1.4 WHILE-Programs and WHILE-Computability.- 1.5 Tape Machines.- 1.6 Stack Machines.- 1.7 Comparison of Number and Word Functions, Church's Thesis.- 1.8 Recursive and Recursively Enumerable Sets.- 1.9 The Standard Numbering ? of P(1).- 1.10 Some Unsolvable Problems.- 2: Type 1 Recursion Theory.- 2.1 The Basic Concepts of Computability Theory.- 2.2 Numberings.- 2.3 Recursive and Recursively Enumerable Sets (Continued).- 2.4 Many-one and One-one Reducibility.- 2.5 The Recursion Theorem.- 2.6 Creative, Productive, Complete Sets.- 2.7 Effective Numberings.- 2.8 Ordinal Trees and Computable Ordinals.- 2.9 Some Applications to Logic.- 2.10 Oracle Machines and Relativized Recursion Theory.- 2.11 Turing Reducibility and the Kleene Hierarchy.- 2.12 Computational Complexity.- 3: Type 2 Theory of Constructivity and Computability.- 3.1 Type 2 Computability Models.- 3.2 Recursion Theory on Baire's Space.- 3.3 Representations.- 3.4 Effective Representations.- 3.5 Complete Partial Orders.- 3.6 Type 1 Computability and Type 2 Computability.- 3.7 Solving Domain Equations.- 3.8 Applications to Analysis.- Index of Notations.