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1 | (2) |
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Chapter 0 On the Choice of Correct Notions for the General Theory |
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3 | (14) |
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0.1 Finite Algorithmic Procedures |
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3 | (4) |
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0.2 FAP and Inductive Definability |
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7 | (1) |
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0.3 FAP and Computation Theories |
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8 | (3) |
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11 | (1) |
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0.5 Recent Developments in Inductive Definability |
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12 | (5) |
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17 | (46) |
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Chapter 1 General Theory: Combinatorial Part |
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19 | (24) |
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19 | (3) |
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1.2 Some Computable Functions |
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22 | (3) |
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1.3 Semicomputable Relations |
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25 | (2) |
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1.4 Computing Over the Integers |
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27 | (2) |
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1.5 Inductively Defined Theories |
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29 | (5) |
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1.6 A Simple Representation Theorem |
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34 | (4) |
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1.7 The First Recursion Theorem |
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38 | (5) |
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Chapter 2 General Theory: Subcomputations |
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43 | (20) |
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43 | (2) |
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2.2 Inductively Defined Theories |
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45 | (3) |
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2.3 The First Recursion Theorem |
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48 | (2) |
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2.4 Semicomputable Relations |
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50 | (2) |
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52 | (2) |
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2.6 Extension of Theories |
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54 | (3) |
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2.7 Faithful Representation |
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57 | (6) |
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63 | (44) |
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Chapter 3 Finite Theories on One Type |
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65 | (25) |
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3.1 The Prewellordering Property |
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65 | (7) |
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72 | (7) |
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3.3 Spector Theories and Inductive Definability |
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79 | (11) |
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Chapter 4 Finite Theories on Two Types |
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90 | (17) |
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4.1 Computation Theories on Two Types |
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90 | (6) |
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4.2 Recursion in a Normal List |
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96 | (3) |
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4.3 Selection in Higher Types |
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99 | (6) |
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4.4 Computation Theories and Second Order Definability |
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105 | (2) |
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107 | (58) |
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Chapter 5 Admissible Prewellorderings |
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109 | (31) |
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5.1 Admissible Prewellorderings and Infinite Theories |
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111 | (6) |
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5.2 The Characterization Theorem |
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117 | (5) |
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5.3 The Imbedding Theorem |
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122 | (4) |
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5.4 Spector Theories Over ω |
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126 | (14) |
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Chapter 6 Degree Structure |
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140 | (25) |
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140 | (9) |
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6.2 The Splitting Theorem |
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149 | (8) |
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157 | (8) |
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165 | (44) |
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Chapter 7 Computations Over Two Types |
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167 | (15) |
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7.1 Computations and Reflection |
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167 | (4) |
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7.2 The General Plus-2 and Plus-1 Theorem |
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171 | (8) |
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7.3 Characterization in Higher Types |
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179 | (3) |
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Chapter 8 Set Recursion and Higher Types |
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182 | (27) |
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182 | (2) |
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184 | (3) |
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8.3 Set Recursion and Kleene-recursion in Higher Types |
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187 | (7) |
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8.4 Degrees of Functionals |
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194 | (9) |
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203 | (6) |
| References |
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209 | (8) |
| Notation |
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217 | (3) |
| Author Index |
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220 | (3) |
| Subject Index |
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223 | |
Lisainfo e-raamatute kohta