Borel liftings of Borel sets: some decidable and undecidable statements
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
2007
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
876 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | "May 2007, volume 187, number 876 (first of 4 numbers)." Includes bibliographical references and index |
| Beschreibung: | VII, 118 S. |
| ISBN: | 9780821839713 |
Internformat
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| 245 | 1 | 0 | |a Borel liftings of Borel sets |b some decidable and undecidable statements |c Gabriel Debs ; Jean Saint Raymond |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2007 | |
| 300 | |a VII, 118 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v 876 | |
| 500 | |a "May 2007, volume 187, number 876 (first of 4 numbers)." | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Borelverzamelingen |2 gtt | |
| 650 | 7 | |a Topologia |2 larpcal | |
| 650 | 4 | |a Borel sets | |
| 650 | 4 | |a Constructibility (Set theory) | |
| 650 | 4 | |a Descriptive set theory | |
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| 830 | 0 | |a Memoirs of the American Mathematical Society |v 876 |w (DE-604)BV008000141 |9 876 | |
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Datensatz im Suchindex
| _version_ | 1804136492577062913 |
|---|---|
| adam_text | Contents
Introduction 1
0.1. Descriptive classes: 2
0.2. An elementary topological problem: 3
0.3. Continuous and Borel liftings: 5
0.4. Main result 7
0.5. Application 1 7
0.6. Application 2 8
0.7. Application 3 9
Chapter 1. A Tree Representation for Borel Sets 11
1.1. Trees 11
1.2. Distinguished subrelation 13
1.3. Canonical mapping of a distinguished subtree 15
1.4. Uniformly distinguished subtree 19
1.5. Tree products 21
1.6. Tree expansions and representations of Borel sets 26
1.7. Regular expansions and representations 30
Chapter 2. A Double Tree Representation for Borel Sets 33
2.1. Double trees 33
2.2. Double tree characterization of E§ sets 38
2.3. Double tree characterization of D(E°) sets 41
2.4. Appendix : extension to Wadge classes 44
Chapter 3. Two Applications of the Tree Representation 49
3.1. Resolution of quasi strategies 49
3.2. Hurewicz type results 55
3.3. A Borel separation result 59
Chapter 4. Borel Liftings of Borel Sets 63
4.1. Borel liftings of bounded rank 63
4.2. Borel liftings of unbounded rank 68
4.3. Solution to Ostrovsky s problem 70
4.4. Borel liftings in coanalytic sets 71
Chapter 5. More Consequences and Reverse Results 75
5.1. Some boudedness principles 76
5.2. Reverse results 80
5.3. Conclusion 86
5.4. Appendix: A Perfect Set Theorem
for a Class of Equivalence Relations 87
V
vi CONTENTS
Chapter 6. Proof of The Main Result 91
6.1. Sketch of the proof 91
6.2. Labeling games with delay 95
6.3. Proof of the basic case 104
6.4. Proof of the general limit case 110
6.5. Proof of the general successor case 112
Bibliography 115
Index 117
|
| adam_txt |
Contents
Introduction 1
0.1. Descriptive classes: 2
0.2. An elementary topological problem: 3
0.3. Continuous and Borel liftings: 5
0.4. Main result 7
0.5. Application 1 7
0.6. Application 2 8
0.7. Application 3 9
Chapter 1. A Tree Representation for Borel Sets 11
1.1. Trees 11
1.2. Distinguished subrelation 13
1.3. Canonical mapping of a distinguished subtree 15
1.4. Uniformly distinguished subtree 19
1.5. Tree products 21
1.6. Tree expansions and representations of Borel sets 26
1.7. Regular expansions and representations 30
Chapter 2. A Double Tree Representation for Borel Sets 33
2.1. Double trees 33
2.2. Double tree characterization of E§ sets 38
2.3. Double tree characterization of D(E°) sets 41
2.4. Appendix : extension to Wadge classes 44
Chapter 3. Two Applications of the Tree Representation 49
3.1. Resolution of quasi strategies 49
3.2. Hurewicz type results 55
3.3. A Borel separation result 59
Chapter 4. Borel Liftings of Borel Sets 63
4.1. Borel liftings of bounded rank 63
4.2. Borel liftings of unbounded rank 68
4.3. Solution to Ostrovsky's problem 70
4.4. Borel liftings in coanalytic sets 71
Chapter 5. More Consequences and Reverse Results 75
5.1. Some boudedness principles 76
5.2. Reverse results 80
5.3. Conclusion 86
5.4. Appendix: A Perfect Set Theorem
for a Class of Equivalence Relations 87
V
vi CONTENTS
Chapter 6. Proof of The Main Result 91
6.1. Sketch of the proof 91
6.2. Labeling games with delay 95
6.3. Proof of the basic case 104
6.4. Proof of the general limit case 110
6.5. Proof of the general successor case 112
Bibliography 115
Index 117 |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:26:17Z |
| indexdate | 2024-07-09T20:57:16Z |
| institution | BVB |
| isbn | 9780821839713 |
| language | English |
| lccn | 2007060664 |
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| physical | VII, 118 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Debs, Gabriel 1952- Verfasser (DE-588)1146947828 aut Borel liftings of Borel sets some decidable and undecidable statements Gabriel Debs ; Jean Saint Raymond Providence, R.I. American Mathematical Society 2007 VII, 118 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 876 "May 2007, volume 187, number 876 (first of 4 numbers)." Includes bibliographical references and index Borelverzamelingen gtt Topologia larpcal Borel sets Constructibility (Set theory) Descriptive set theory Borel-Menge (DE-588)4146323-7 gnd rswk-swf Borel-Menge (DE-588)4146323-7 s DE-604 Saint Raymond, Jean Verfasser aut Memoirs of the American Mathematical Society 876 (DE-604)BV008000141 876 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015631104&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Debs, Gabriel 1952- Saint Raymond, Jean Borel liftings of Borel sets some decidable and undecidable statements Memoirs of the American Mathematical Society Borelverzamelingen gtt Topologia larpcal Borel sets Constructibility (Set theory) Descriptive set theory Borel-Menge (DE-588)4146323-7 gnd |
| subject_GND | (DE-588)4146323-7 |
| title | Borel liftings of Borel sets some decidable and undecidable statements |
| title_auth | Borel liftings of Borel sets some decidable and undecidable statements |
| title_exact_search | Borel liftings of Borel sets some decidable and undecidable statements |
| title_exact_search_txtP | Borel liftings of Borel sets some decidable and undecidable statements |
| title_full | Borel liftings of Borel sets some decidable and undecidable statements Gabriel Debs ; Jean Saint Raymond |
| title_fullStr | Borel liftings of Borel sets some decidable and undecidable statements Gabriel Debs ; Jean Saint Raymond |
| title_full_unstemmed | Borel liftings of Borel sets some decidable and undecidable statements Gabriel Debs ; Jean Saint Raymond |
| title_short | Borel liftings of Borel sets |
| title_sort | borel liftings of borel sets some decidable and undecidable statements |
| title_sub | some decidable and undecidable statements |
| topic | Borelverzamelingen gtt Topologia larpcal Borel sets Constructibility (Set theory) Descriptive set theory Borel-Menge (DE-588)4146323-7 gnd |
| topic_facet | Borelverzamelingen Topologia Borel sets Constructibility (Set theory) Descriptive set theory Borel-Menge |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015631104&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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