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E-raamat: Higher Recursion Theory

(Harvard University, Massachusetts)
  • Formaat: PDF+DRM
  • Sari: Perspectives in Logic
  • Ilmumisaeg: 02-Mar-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316731741
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Higher Recursion TheorySuurem pilt
  • Formaat: PDF+DRM
  • Sari: Perspectives in Logic
  • Ilmumisaeg: 02-Mar-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316731741
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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. This volume, the second publication in the Perspectives in Logic series, is an almost self-contained introduction to higher recursion theory, in which the reader is only assumed to know the basics of classical recursion theory. The book is divided into four parts: hyperarithmetic sets, metarecursion, -recursion, and E-recursion. This text is essential reading for all researchers in the field.

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This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
Part A Hyperarithmetic Sets
1(112)
Chapter I Constructive Ordinals and Π11 Sets
3(19)
1 Analytical Predicates
3(5)
2 Notations for Ordinals
8(2)
3 Effective Transfinite Recursion
10(5)
4 Recursive Ordinals
15(3)
5 Ordinal Analysis of Π11 Sets
18(4)
Chapter II The Hyperarithmetic Hierarchy
22(30)
1 Hyperarithmetic Implies Δ11
22(6)
2 Δ11 Implies Hyperarithmetic
28(4)
3 Selection and Reduction
32(5)
4 Π02 Singletons
37(5)
5 Hyperarithmetic Reducibility
42(4)
6 Incomparable Hyperdegrees Via Measure
46(2)
7 The Hyperjump
48(4)
Chapter III Σ11 Predicates of Reals
52(36)
1 Basis Theorems
52(3)
2 Unique Notations for Ordinals
55(4)
3 Hyperarithmetic Quantifiers
59(3)
4 The Ramified Analytic Hierarchy
62(8)
5 Kreisel Compactness
70(1)
6 Perfect Subsets of Σ11 Sets
71(3)
7 Kreisel's Basis Theorem
74(2)
8 Inductive Definitions
76(5)
9 Π11 Singletons
81(7)
Chapter IV Measure and Forcing
88(25)
1 Measure-Theoretic Uniformity
88(4)
2 Measure-Theoretic Basis Theorems
92(2)
3 Cohen Forcing
94(4)
4 Perfect Forcing
98(5)
5 Minimal Hyperdegrees
103(4)
6 Louveau Separation
107(6)
Part B Metarecursion
113(36)
Chapter V Metarecursive Enumerability
115(20)
1 Fundamentals of Metarecursion
115(6)
2 Metafinite Computations
121(3)
3 Relative Metarecursiveness
124(5)
4 Regularity
129(6)
Chapter VI Hyperregularity and Priority
135(14)
1 Hyperregular Sets
135(3)
2 Two Priority Arguments
138(8)
3 Simpson's Dichotomy
146(3)
Part C α-Recursion
149(82)
Chapter VII Admissibility and Regularity
151(24)
1 Σ1 Admissibility
151(6)
2 The Σ1 Projectum
157(4)
3 Relative α-Recursiveness
161(4)
4 Existence of Regular Sets
165(2)
5 Hyperregularity
167(8)
Chapter VIII Priority Arguments
175(29)
1 α-Finite Injury via α*
175(3)
2 α-Finite Injury and Tameness
178(6)
3 Dynamic Versus Fine-Structure
184(10)
4 Σ1 Doing the Work of Σ2
194(10)
Chapter IX Splitting, Density and Beyond
204(27)
1 Shore's Splitting Theorem
204(3)
2 Further Fine Structure
207(5)
3 Density for ω
212(4)
4 Preliminaries to α-Density
216(2)
5 Shore's Density Theorem
218(9)
6 β-Recursion Theory
227(4)
Part D E-Recursion
231(108)
Chapter X E-Closed Structures
233(26)
1 Partial E-Recursive Functions
233(4)
2 Computations
237(5)
3 Reflection
242(2)
4 Gandy Selection
244(5)
5 Moschovakis Witnesses
249(10)
Chapter XI Forcing Computations to Converge
259(24)
1 Set Forcing over L(κ)
259(6)
2 Countably Closed Forcing
265(5)
3 Enumerable Forcing Relations
270(3)
4 Countable-Chain-Condition Forcing
273(6)
5 Normann Selection and Singular Cardinals
279(2)
6 Further Forcing
281(2)
Chapter XII Selection and k-Sections
283(26)
1 Grilliot Selection
284(3)
2 Moschovakis Selection
287(3)
3 Plus-One Theorems
290(9)
4 Harrington's Plus-Two Theorem
299(5)
5 Selection with Additional Predicates
304(5)
Chapter XIII E-Recursively Enumerable Degrees
309(30)
1 Regular Sets
309(4)
2 Projecta and Cofinalities
313(12)
3 van de Wiele's Theorem
325(3)
4 Post's Problem for E-Recursion
328(5)
5 Slaman's Splitting and Density Theorems
333(6)
Bibliography 339(4)
Subject Index 343
Gerald E. Sacks works in the Department of Mathematics at Harvard University, Massachusetts and at the Massachusetts Institute of Technology.
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