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Computability Computable Functions, Logic, and the Foundations of Mathematics, with Computability: A Timeline

ISBN-10: 0534546447
ISBN-13: 9780534546441
Edition: 2nd 2000
List price: $37.95
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Description: This intuitive introduction to computability theory contains numerous background discussions which introduce the reader to the folkloric and philosophical aspects of recursion theory and logic.

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Book details

List price: $37.95
Edition: 2nd
Copyright year: 2000
Publisher: Wadsworth
Publication date: 7/12/1999
Binding: Paperback
Pages: 352
Size: 7.00" wide x 9.25" long x 0.50" tall
Weight: 1.232
Language: English

This intuitive introduction to computability theory contains numerous background discussions which introduce the reader to the folkloric and philosophical aspects of recursion theory and logic.

Preface. Acknowledgements. I. THE FUNDAMENTALS. 1. Paradoxes. 2. What do the Paradoxes Mean? 3. Whole Numbers. 4. Functions. 5. Proofs. 6. Infinite Collections? 7. Hilber "On the Infinite." II. COMPUTABLE FUNCTIONS. 8. Computability. 9. Turing Machines. 10. The Most Amazing Fact and Church's Thesis. 11. Primitive Recursive Functions. 12. The Grzegorczyk Hierarchy. 13. Multiple Recursion. 14. The Least Search Operator. 15. Partial Recursive Functions. 16. Numbering and Partial Recursive Functions. 17. Listability. 18. Turing Machines Computable = Partial Recursive. III. LOGIC AND ARITHMETIC. 19. Propositional Logic. 20. An Overview of First-Order Logic and Gdel's Theorems. 21. First-Order Arithmetic. 22. Functions Representable in Formal Arithmetic. 23. The Undecidability of Arithmetic. 24. The Unprovability of Consistency. IV. CHURCH'S THESIS AND CONSTRUCTIVE MATHEMATICS. 25. Church's Thesis. 26. Constructivist Views of Mathematics. Bibliography. GLOSSARY AND INDEX OF NOTATION. INDEX.

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