Recursion Theory for Metamathematics

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Oxford University Press, Jan 28, 1993 - Mathematics - 184 pages
This work is a sequel to the author's Gödel's Incompleteness Theorems, though it can be read independently by anyone familiar with Gödel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
 

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Contents

0 Prerequisites
1
Recursive Enumerability and Recursivity
24
Undecidability and Recursive Inseparability
38
Indexing
48
Generative Sets and Creative Systems
58
Double Generativity and Complete Effective Inseparability
67
Universal and Doubly Universal Systems
82
Shepherdson Revisited
89
Recursion Theorems
94
Symmetric and Double Recursion Theorems
105
Productivity and Double Productivity
120
Three Special Topics
128
Uniform Gödelization
141
References
159
Index
161
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Page viii - theorems of 1960 can be proved without appeal to the recursion theorem or any other fixed point argument.
Page ix - sentential and double sentential recursion properties, Rosser fixed point properties, uniform incompleteness) and

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