Author | Hermes, Hans. author |
---|---|
Title | Enumerability ยท Decidability Computability [electronic resource] : An Introduction to the Theory of Recursive Functions / by Hans Hermes |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1969 |
Edition | Second revised Edition |
Connect to | http://dx.doi.org/10.1007/978-3-642-46178-1 |
Descript | XII, 250 p. online resource |
1. Introductory Reflections on Algorithms -- ยง 1. The Concept of Algorithm -- ยง 2. The Fundamental Concepts of the Theory of Constructivity -- ยง 3. The Concept of Turing Machine as an Exact Mathematical Substitute for the Concept of Algorithm -- ยง 4. Historical Remarks -- 2. Turing Machines -- ยง 5. Definition of Turing Machines -- ยง 6. Precise Definition of Constructive Concepts by means of Turing Machines -- ยง 7. Combination of Turing Machines -- ยง 8. Special Turing Machines -- ยง 9. Examples of Turing-Computability and Turing-Decidability -- 3. ?-Recursive Functions -- ยง 10. Primitive Recursive Functions -- ยง 11. Primitive Recursive Predicates -- ยง 12. The ?-Operator -- ยง 13. Example of a Computable Function which is not Primitive Recursive -- ยง 14. ?-Recursive Functions and Predicates -- 4. The Equivalence of Turing-Computability and ?-Recursiveness -- ยง 15. Survey. Standard Turing-Computability -- ยง 16. The Turing-Computability of ?-Recursive Functions -- ยง 17. Gรถdel Numbering of Turing Machines -- ยง 18. The ?-Recursiveness of Turing-Computable Functions. Kleeneโs Normal Form -- 5. Recursive Functions -- ยง 19. Definition of Recursive Functions -- ยง 20. The Recursiveness of ?-Recursive Functions -- ยง 21. The ?-Recursiveness of Recursive Functions -- 6. Undecidable Predicates -- ยง 22. Simple Undecidable Predicates -- ยง 23. The Unsolvability of the Word Problem for Semi-Thue Systems and Thue Systems -- ยง 24. The Predicate Calculus -- ยง 25. The Undecidability of the Predicate Calculus -- ยง 26. The Incompleteness of the Predicate Calculus of the Second Order -- ยง 27. The Undecidability and Incompleteness of Arithmetic -- 7. Miscellaneous -- ยง 28. Enumerable Predicates -- ยง 29. Arithmetical Predicates -- ยง 30. Universal Turing Machines -- ยง 31. ?-K-Definability -- ยง 32. The Minimal Logic of Fitch -- ยง 33. Further Precise Mathematical Replacements of the Concept of Algorithm -- ยง 34. Recursive Analysis -- Author and Subject Index