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Recursion Theory

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Reports new developments in symbolic logic, broadly interpreted quickly, informally, and at a high level. Paper.

Author(s): Joseph R. Shoenfield
Series: Lecture Notes in Logic
Publisher: Springer-Verlag
Year: 1993

Language: English
Pages: 94

Introduction......Page 7
Contents......Page 9
1. Computability......Page 11
2. Functions and Relations......Page 12
3. The Basic Machine......Page 13
4. Macros......Page 15
5. Closure Properties......Page 18
6. Definitions of Recursive Functions......Page 21
7. Codes......Page 26
8. Indices......Page 30
9. Church's Thesis......Page 36
10. Word Problems......Page 38
11. Undecidable Theories......Page 42
12. Relative Recursion......Page 49
13. The Arithmetical Hierarchy......Page 53
14. Recursively Enumerable Relations......Page 58
15. Degrees......Page 63
16. Evaluation of Degrees......Page 69
17. Large RE Sets......Page 73
18. Functions of Reals......Page 77
19. The Analytical Hierarchy......Page 81
20. The Projective Hierarchy......Page 84
Suggestions for Further Reading......Page 89
Index......Page 91