Higher recursion theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1990
|
| Series: | Perspectives in mathematical logic
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 344 S. |
| ISBN: | 3540193057 0387193057 |
Staff View
MARC
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| 245 | 1 | 0 | |a Higher recursion theory |c Gerald E. Sacks |
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| 490 | 0 | |a Perspectives in mathematical logic | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Part A. Hyperarithmetic Sets 1
Chapter I. Constructive Ordinals and nj Sets 3
1. Analytical Predicates 3
2. Notations for Ordinals 8
3. Effective Transfinite Recursion 10
4. Recursive Ordinals 15
5. Ordinal Analysis of nj Sets 18
Chapter II. The Hyperarithmetic Hierarchy 22
1. Hyperarithmetic Implies A} 22
2. A} Implies Hyperarithmetic 28
3. Selection and Reduction 32
4. IT5 Singletons 37
5. Hyperarithmetic Reducibility 42
6. Incomparable Hyperdegrees Via Measure 46
7. The Hyperjump 48
Chapter III. S { Predicates of Reals 52
1. Basis Theorems 52
2. Unique Notations for Ordinals 55
3. Hyperarithmetic Quantifiers 59
4. The Ramified Analytic Hierarchy 62
5. Kreisel Compactness 70
6. Perfect Subsets of Z} Sets 71
7. Kreisel s Basis Theorem 74
8. Inductive Definitions 76
9. nj Singletons 81
XIV Contents
Chapter IV Measure and Forcing 88
1. Measure Theoretic Uniformity 88
2. Measure Theoretic Basis Theorems 92
3. Cohen Forcing 94
4. Perfect Forcing 98
5. Minimal Hyperdegrees 103
6. Louveau Separation 107
Part B. Metarecursion 113
Chapter V Metarecursive Enumerability ....115
1. Fundamentals of Metarecursion ...115
2. Metafmite Computations 121
3. Relative Metarecursiveness 124
4. Regularity 129
Chapter VI. Hyperregularity and Priority 135
1. Hyperregular Sets 135
2. Two Priority Arguments 138
3. Simpson s Dichotomy 146
Part C. a Recursion .149
Chapter VII. Admissibility and Regularity ....151
1. Zx Admissibility ....151
2. TheX^ Projectum 157
3. Relative a Recursiveness 161
4. Existence of Regular Sets 165
5. Hyperregularity 167
Chapter VIII. Priority Arguments 175
1. a Finite Injury via a* 175
2. a Finite Injury and Tameness 178
3. Dynamic Versus Fine Structure 184
4. S , Doing the Work of S2 194
Contents XV
Chapter IX. Splitting, Density and Beyond 204
1. Shore s Splitting Theorem 204
2. Further Fine Structure 207
3. Density for a 212
4. Preliminaries to a Density 216
5. Shore s Density Theorem 218
6. /ï Recursion Theory 227
PartD. ^ Recursion 231
Chapter X. £ Closed Structures 233
1. Partial ^ Recursive Functions 233
2. Computations 237
3. Reflection 242
4. Gandy Selection 244
5. Moschovakis Witnesses 249
Chapter XL Forcing Computations to Converge 259
1. Set Forcing over L (k) 259
2. Countably Closed Forcing 265
3. Enumerable Forcing Relations 270
4. Countable Chain Condition Forcing 273
5. Normann Selection and Singular Cardinals 279
6. Further Forcing 281
Chapter XII. Selection and /c Sections 283
1. Grilliot Selection 284
2. Moschovakis Selection 287
3. Plus One Theorems 290
4. Harrington s Plus Two Theorem 299
5. Selection with Additional Predicates 304
Chapter XIII. ^ Recursively Enumerable Degrees 309
1. Regular Sets 309
2. Projecta and Cofinalities 313
3. van de Wiele s Theorem 325
4. Post s Problem for ^ Recursion 328
5. Slaman s Splitting and Density Theorems 333
Bibliography 339
Subject Index 343
|
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| dewey-sort | 3511.3 |
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| discipline | Informatik Mathematik Philosophie |
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| id | DE-604.BV001801488 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:36:10Z |
| institution | BVB |
| isbn | 3540193057 0387193057 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001210673 |
| oclc_num | 19130395 |
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| owner_facet | DE-91 DE-BY-TUM DE-12 DE-703 DE-739 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | XV, 344 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Springer |
| record_format | marc |
| series2 | Perspectives in mathematical logic |
| spelling | Sacks, Gerald E. 1933-2019 Verfasser (DE-588)128780770 aut Higher recursion theory Gerald E. Sacks Berlin [u.a.] Springer 1990 XV, 344 S. txt rdacontent n rdamedia nc rdacarrier Perspectives in mathematical logic Récursivité, théorie de la ram Recursion theory Rekursionstheorie (DE-588)4122329-9 gnd rswk-swf Rekursionstheorie (DE-588)4122329-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001210673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sacks, Gerald E. 1933-2019 Higher recursion theory Récursivité, théorie de la ram Recursion theory Rekursionstheorie (DE-588)4122329-9 gnd |
| subject_GND | (DE-588)4122329-9 |
| title | Higher recursion theory |
| title_auth | Higher recursion theory |
| title_exact_search | Higher recursion theory |
| title_full | Higher recursion theory Gerald E. Sacks |
| title_fullStr | Higher recursion theory Gerald E. Sacks |
| title_full_unstemmed | Higher recursion theory Gerald E. Sacks |
| title_short | Higher recursion theory |
| title_sort | higher recursion theory |
| topic | Récursivité, théorie de la ram Recursion theory Rekursionstheorie (DE-588)4122329-9 gnd |
| topic_facet | Récursivité, théorie de la Recursion theory Rekursionstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001210673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sacksgeralde higherrecursiontheory |