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E-grāmata: General Recursion Theory: An Axiomatic Approach

(Universitetet i Oslo)
  • Formāts: PDF+DRM
  • Sērija : Perspectives in Logic
  • Izdošanas datums: 02-Mar-2017
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781316731642
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General Recursion Theory: An Axiomatic ApproachPalielināt
  • Formāts: PDF+DRM
  • Sērija : Perspectives in Logic
  • Izdošanas datums: 02-Mar-2017
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781316731642
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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the tenth publication in the Perspectives in Logic series, Jens E. Fenstad takes an axiomatic approach to present a unified and coherent account of the many and various parts of general recursion theory. The main core of the book gives an account of the general theory of computations. The author then moves on to show how computation theories connect with and unify other parts of general recursion theory. Some mathematical maturity is required of the reader, who is assumed to have some acquaintance with recursion theory. This book is ideal for a second course in the subject.

Papildus informācija

This volume presents a unified and coherent account of the many and various parts of general recursion theory.
Pons Asinorum 1(2)
Chapter 0 On the Choice of Correct Notions for the General Theory
3(14)
0.1 Finite Algorithmic Procedures
3(4)
0.2 FAP and Inductive Definability
7(1)
0.3 FAP and Computation Theories
8(3)
0.4 Platek's Thesis
11(1)
0.5 Recent Developments in Inductive Definability
12(5)
Part A General Theory
17(46)
Chapter 1 General Theory: Combinatorial Part
19(24)
1.1 Basic Definitions
19(3)
1.2 Some Computable Functions
22(3)
1.3 Semicomputable Relations
25(2)
1.4 Computing Over the Integers
27(2)
1.5 Inductively Defined Theories
29(5)
1.6 A Simple Representation Theorem
34(4)
1.7 The First Recursion Theorem
38(5)
Chapter 2 General Theory: Subcomputations
43(20)
2.1 Subcomputations
43(2)
2.2 Inductively Defined Theories
45(3)
2.3 The First Recursion Theorem
48(2)
2.4 Semicomputable Relations
50(2)
2.5 Finiteness
52(2)
2.6 Extension of Theories
54(3)
2.7 Faithful Representation
57(6)
Part B Finite Theories
63(44)
Chapter 3 Finite Theories on One Type
65(25)
3.1 The Prewellordering Property
65(7)
3.2 Spector Theories
72(7)
3.3 Spector Theories and Inductive Definability
79(11)
Chapter 4 Finite Theories on Two Types
90(17)
4.1 Computation Theories on Two Types
90(6)
4.2 Recursion in a Normal List
96(3)
4.3 Selection in Higher Types
99(6)
4.4 Computation Theories and Second Order Definability
105(2)
Part C Infinite Theories
107(58)
Chapter 5 Admissible Prewellorderings
109(31)
5.1 Admissible Prewellorderings and Infinite Theories
111(6)
5.2 The Characterization Theorem
117(5)
5.3 The Imbedding Theorem
122(4)
5.4 Spector Theories Over ω
126(14)
Chapter 6 Degree Structure
140(25)
6.1 Basic Notions
140(9)
6.2 The Splitting Theorem
149(8)
6.3 The Theory Extended
157(8)
Part D Higher Types
165(44)
Chapter 7 Computations Over Two Types
167(15)
7.1 Computations and Reflection
167(4)
7.2 The General Plus-2 and Plus-1 Theorem
171(8)
7.3 Characterization in Higher Types
179(3)
Chapter 8 Set Recursion and Higher Types
182(27)
8.1 Basic Definitions
182(2)
8.2 Companion Theory
184(3)
8.3 Set Recursion and Kleene-recursion in Higher Types
187(7)
8.4 Degrees of Functionals
194(9)
8.5 Epilogue
203(6)
References 209(8)
Notation 217(3)
Author Index 220(3)
Subject Index 223
Jens E. Fenstad works in the Department of Mathematics at the University of Oslo.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97813167316422e.html
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