Inner models and large cardinals /:
Biographical note: Professor Martin Zeman, Institut für formale Logik, University Vienna, Vienna, Austria.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; New York :
Walter de Gruyter,
2002.
|
| Schriftenreihe: | De Gruyter series in logic and its applications,
5 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Biographical note: Professor Martin Zeman, Institut für formale Logik, University Vienna, Vienna, Austria. Main description: This volume is an introduction to inner model theory, an area of set theory which is concerned with fine structural inner models reflecting large cardinal properties of the set theoretic universe. The monograph contains a detailed presentation of general fine structure theory as well as a modern approach to the construction of small core models, namely those models containing at most one strong cardinal, together with some of their applications. The final part of the book is devoted to a new approach encompassing large inner models which admit many Woodin cardinals. The exposition is self-contained and does not assume any special prerequisities, which should make the text comprehensible not only to specialists but also to advanced students in Mathematical Logic and Set Theory. Review text: "Insgesamt ist Zeman ein ausgezeichnetes Lehrbuch über Kernmodelltheorie gelungen. Es ist sehr gut zum Selbststudium geeignet."H.-D. Donder, Jahresbericht der Deutschen Mathematiker-Vereinigung 106, 3-2004 |
| Beschreibung: | 1 online resource (xi, 369 pages) |
| Bibliographie: | Includes bibliographical references (pages 359-363) and index. |
| ISBN: | 9783110857818 3110857812 |
| ISSN: | 1438-1893 ; |
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| 100 | 1 | |a Zeman, Martin, |d 1964- |1 https://id.oclc.org/worldcat/entity/E39PCjJTgd3qYWpWxr47HfWPXq |0 http://id.loc.gov/authorities/names/n2001014688 | |
| 245 | 1 | 0 | |a Inner models and large cardinals / |c Martin Zeman. |
| 260 | |a Berlin ; |a New York : |b Walter de Gruyter, |c 2002. | ||
| 300 | |a 1 online resource (xi, 369 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 0 | |a De Gruyter series in logic and its applications, |x 1438-1893 ; |v 5 | |
| 504 | |a Includes bibliographical references (pages 359-363) and index. | ||
| 520 | |a Biographical note: Professor Martin Zeman, Institut für formale Logik, University Vienna, Vienna, Austria. | ||
| 520 | |a Main description: This volume is an introduction to inner model theory, an area of set theory which is concerned with fine structural inner models reflecting large cardinal properties of the set theoretic universe. The monograph contains a detailed presentation of general fine structure theory as well as a modern approach to the construction of small core models, namely those models containing at most one strong cardinal, together with some of their applications. The final part of the book is devoted to a new approach encompassing large inner models which admit many Woodin cardinals. The exposition is self-contained and does not assume any special prerequisities, which should make the text comprehensible not only to specialists but also to advanced students in Mathematical Logic and Set Theory. | ||
| 520 | |a Review text: "Insgesamt ist Zeman ein ausgezeichnetes Lehrbuch über Kernmodelltheorie gelungen. Es ist sehr gut zum Selbststudium geeignet."H.-D. Donder, Jahresbericht der Deutschen Mathematiker-Vereinigung 106, 3-2004 | ||
| 505 | 0 | |a Preface -- 1 Fine Structure -- 1.1 Acceptable J-Structures -- 1.2 The V1-Projectum -- 1.3 Downward Extension of Embeddings Lemmata -- 1.4 Upward Extension of Embeddings Lemma -- 1.5 Iterated Projecta -- 1.6 V*-Relations -- 1.7 V0(n)-Embeddings -- 1.8 Substitution and Good Functions -- 1.9 Standard Parameters -- 1.10 Two Applications to L -- 1.11 More on Downward Extensions of Embeddings -- 1.12 Witnesses and Solidity -- Notes -- 2 Extenders and Coherent Structures -- 2.1 Extenders -- 2.2 The Hypermeasure Representation of Extenders -- 2.3 Amenability -- 2.4 Coherent Structures. | |
| 505 | 8 | |a 2.5 Extendibility -- 2.6 Strong Cardinals -- Notes -- 3 Fine Ultrapowers -- 3.1 The *-Ultrapower Construction -- 3.2 Some Special Preservation Properties -- 3.3 When F Is Close to M -- 3.4 Extendibility -- 3.5 k-Ultrapowers -- 3.6 Pseudoultrapowers -- Notes -- 4 Mice and Iterability -- 4.1 Premice -- 4.2 Iterations -- 4.3 Copying and the Dodd-Jensen Lemma -- 4.4 Comparison Process -- 4.5 Some Iterability Criteria -- 4.6 Bicephali -- Notes -- 5 Solidity and Condensation -- 5.1 Cores and Coiterations -- 5.2 The Solidity Theorem -- 5.3 Consequences of Solidity -- 5.4 The Canonical Ordering of Mice. | |
| 505 | 8 | |a 5.5 Condensation Lemma -- 5.6 Upwards Extensions to Premice -- Notes -- 6 Extender Models -- 6.1 Extender Models and Iterations -- 6.2 The Canonical Ordering of Weasels -- 6.3 Universality -- 6.4 The Model Kc -- 6.5 0** -- 6.6 Weak Covering -- Notes -- 7 The Core Model -- 7.1 Inductive Definition of K -- 7.2 Steel's Definition of K -- 7.3 The Existence of K -- 7.4 Embeddings of K and Generic Absoluteness -- 7.5 Weak Covering for K -- Notes -- 8 One Strong Cardinal -- 8.1 Premice -- 8.2 Properties of Mice -- 8.3 Extender Models up to One Strong Cardinal -- Notes -- 9 Overlapping Extenders. | |
| 505 | 8 | |a 9.1 Premice and Iteration Trees -- 9.2 Copying and the Dodd-Jensen Property -- 9.3 Solidity and Condensation -- 9.4 Uniqueness of Weil-Founded Branches -- 9.5 Towards the Ultimate Model Kc -- Notes -- Bibliography -- Index. | |
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| contents | Preface -- 1 Fine Structure -- 1.1 Acceptable J-Structures -- 1.2 The V1-Projectum -- 1.3 Downward Extension of Embeddings Lemmata -- 1.4 Upward Extension of Embeddings Lemma -- 1.5 Iterated Projecta -- 1.6 V*-Relations -- 1.7 V0(n)-Embeddings -- 1.8 Substitution and Good Functions -- 1.9 Standard Parameters -- 1.10 Two Applications to L -- 1.11 More on Downward Extensions of Embeddings -- 1.12 Witnesses and Solidity -- Notes -- 2 Extenders and Coherent Structures -- 2.1 Extenders -- 2.2 The Hypermeasure Representation of Extenders -- 2.3 Amenability -- 2.4 Coherent Structures. 2.5 Extendibility -- 2.6 Strong Cardinals -- Notes -- 3 Fine Ultrapowers -- 3.1 The *-Ultrapower Construction -- 3.2 Some Special Preservation Properties -- 3.3 When F Is Close to M -- 3.4 Extendibility -- 3.5 k-Ultrapowers -- 3.6 Pseudoultrapowers -- Notes -- 4 Mice and Iterability -- 4.1 Premice -- 4.2 Iterations -- 4.3 Copying and the Dodd-Jensen Lemma -- 4.4 Comparison Process -- 4.5 Some Iterability Criteria -- 4.6 Bicephali -- Notes -- 5 Solidity and Condensation -- 5.1 Cores and Coiterations -- 5.2 The Solidity Theorem -- 5.3 Consequences of Solidity -- 5.4 The Canonical Ordering of Mice. 5.5 Condensation Lemma -- 5.6 Upwards Extensions to Premice -- Notes -- 6 Extender Models -- 6.1 Extender Models and Iterations -- 6.2 The Canonical Ordering of Weasels -- 6.3 Universality -- 6.4 The Model Kc -- 6.5 0** -- 6.6 Weak Covering -- Notes -- 7 The Core Model -- 7.1 Inductive Definition of K -- 7.2 Steel's Definition of K -- 7.3 The Existence of K -- 7.4 Embeddings of K and Generic Absoluteness -- 7.5 Weak Covering for K -- Notes -- 8 One Strong Cardinal -- 8.1 Premice -- 8.2 Properties of Mice -- 8.3 Extender Models up to One Strong Cardinal -- Notes -- 9 Overlapping Extenders. 9.1 Premice and Iteration Trees -- 9.2 Copying and the Dodd-Jensen Property -- 9.3 Solidity and Condensation -- 9.4 Uniqueness of Weil-Founded Branches -- 9.5 Towards the Ultimate Model Kc -- Notes -- Bibliography -- Index. |
| ctrlnum | (OCoLC)815507724 |
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| dewey-search | 511.3/22 |
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| discipline | Mathematik |
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| indexdate | 2024-11-27T13:25:01Z |
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| issn | 1438-1893 ; |
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| series2 | De Gruyter series in logic and its applications, |
| spelling | Zeman, Martin, 1964- https://id.oclc.org/worldcat/entity/E39PCjJTgd3qYWpWxr47HfWPXq http://id.loc.gov/authorities/names/n2001014688 Inner models and large cardinals / Martin Zeman. Berlin ; New York : Walter de Gruyter, 2002. 1 online resource (xi, 369 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter series in logic and its applications, 1438-1893 ; 5 Includes bibliographical references (pages 359-363) and index. Biographical note: Professor Martin Zeman, Institut für formale Logik, University Vienna, Vienna, Austria. Main description: This volume is an introduction to inner model theory, an area of set theory which is concerned with fine structural inner models reflecting large cardinal properties of the set theoretic universe. The monograph contains a detailed presentation of general fine structure theory as well as a modern approach to the construction of small core models, namely those models containing at most one strong cardinal, together with some of their applications. The final part of the book is devoted to a new approach encompassing large inner models which admit many Woodin cardinals. The exposition is self-contained and does not assume any special prerequisities, which should make the text comprehensible not only to specialists but also to advanced students in Mathematical Logic and Set Theory. Review text: "Insgesamt ist Zeman ein ausgezeichnetes Lehrbuch über Kernmodelltheorie gelungen. Es ist sehr gut zum Selbststudium geeignet."H.-D. Donder, Jahresbericht der Deutschen Mathematiker-Vereinigung 106, 3-2004 Preface -- 1 Fine Structure -- 1.1 Acceptable J-Structures -- 1.2 The V1-Projectum -- 1.3 Downward Extension of Embeddings Lemmata -- 1.4 Upward Extension of Embeddings Lemma -- 1.5 Iterated Projecta -- 1.6 V*-Relations -- 1.7 V0(n)-Embeddings -- 1.8 Substitution and Good Functions -- 1.9 Standard Parameters -- 1.10 Two Applications to L -- 1.11 More on Downward Extensions of Embeddings -- 1.12 Witnesses and Solidity -- Notes -- 2 Extenders and Coherent Structures -- 2.1 Extenders -- 2.2 The Hypermeasure Representation of Extenders -- 2.3 Amenability -- 2.4 Coherent Structures. 2.5 Extendibility -- 2.6 Strong Cardinals -- Notes -- 3 Fine Ultrapowers -- 3.1 The *-Ultrapower Construction -- 3.2 Some Special Preservation Properties -- 3.3 When F Is Close to M -- 3.4 Extendibility -- 3.5 k-Ultrapowers -- 3.6 Pseudoultrapowers -- Notes -- 4 Mice and Iterability -- 4.1 Premice -- 4.2 Iterations -- 4.3 Copying and the Dodd-Jensen Lemma -- 4.4 Comparison Process -- 4.5 Some Iterability Criteria -- 4.6 Bicephali -- Notes -- 5 Solidity and Condensation -- 5.1 Cores and Coiterations -- 5.2 The Solidity Theorem -- 5.3 Consequences of Solidity -- 5.4 The Canonical Ordering of Mice. 5.5 Condensation Lemma -- 5.6 Upwards Extensions to Premice -- Notes -- 6 Extender Models -- 6.1 Extender Models and Iterations -- 6.2 The Canonical Ordering of Weasels -- 6.3 Universality -- 6.4 The Model Kc -- 6.5 0** -- 6.6 Weak Covering -- Notes -- 7 The Core Model -- 7.1 Inductive Definition of K -- 7.2 Steel's Definition of K -- 7.3 The Existence of K -- 7.4 Embeddings of K and Generic Absoluteness -- 7.5 Weak Covering for K -- Notes -- 8 One Strong Cardinal -- 8.1 Premice -- 8.2 Properties of Mice -- 8.3 Extender Models up to One Strong Cardinal -- Notes -- 9 Overlapping Extenders. 9.1 Premice and Iteration Trees -- 9.2 Copying and the Dodd-Jensen Property -- 9.3 Solidity and Condensation -- 9.4 Uniqueness of Weil-Founded Branches -- 9.5 Towards the Ultimate Model Kc -- Notes -- Bibliography -- Index. Constructibility (Set theory) http://id.loc.gov/authorities/subjects/sh85031342 Large cardinals (Mathematics) http://id.loc.gov/authorities/subjects/sh94004021 Constructibilité (Théorie des ensembles) Grands cardinaux (Nombres) MATHEMATICS Set Theory. bisacsh Constructibility (Set theory) fast Large cardinals (Mathematics) fast Constructibility (Set theory) Large cardinals (Mathematics) Print version: Zeman, Martin, 1964- Inner models and large cardinals. Berlin ; New York : Walter de Gruyter, 2002 (DLC) 2001047562 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=559707 Volltext |
| spellingShingle | Zeman, Martin, 1964- Inner models and large cardinals / Preface -- 1 Fine Structure -- 1.1 Acceptable J-Structures -- 1.2 The V1-Projectum -- 1.3 Downward Extension of Embeddings Lemmata -- 1.4 Upward Extension of Embeddings Lemma -- 1.5 Iterated Projecta -- 1.6 V*-Relations -- 1.7 V0(n)-Embeddings -- 1.8 Substitution and Good Functions -- 1.9 Standard Parameters -- 1.10 Two Applications to L -- 1.11 More on Downward Extensions of Embeddings -- 1.12 Witnesses and Solidity -- Notes -- 2 Extenders and Coherent Structures -- 2.1 Extenders -- 2.2 The Hypermeasure Representation of Extenders -- 2.3 Amenability -- 2.4 Coherent Structures. 2.5 Extendibility -- 2.6 Strong Cardinals -- Notes -- 3 Fine Ultrapowers -- 3.1 The *-Ultrapower Construction -- 3.2 Some Special Preservation Properties -- 3.3 When F Is Close to M -- 3.4 Extendibility -- 3.5 k-Ultrapowers -- 3.6 Pseudoultrapowers -- Notes -- 4 Mice and Iterability -- 4.1 Premice -- 4.2 Iterations -- 4.3 Copying and the Dodd-Jensen Lemma -- 4.4 Comparison Process -- 4.5 Some Iterability Criteria -- 4.6 Bicephali -- Notes -- 5 Solidity and Condensation -- 5.1 Cores and Coiterations -- 5.2 The Solidity Theorem -- 5.3 Consequences of Solidity -- 5.4 The Canonical Ordering of Mice. 5.5 Condensation Lemma -- 5.6 Upwards Extensions to Premice -- Notes -- 6 Extender Models -- 6.1 Extender Models and Iterations -- 6.2 The Canonical Ordering of Weasels -- 6.3 Universality -- 6.4 The Model Kc -- 6.5 0** -- 6.6 Weak Covering -- Notes -- 7 The Core Model -- 7.1 Inductive Definition of K -- 7.2 Steel's Definition of K -- 7.3 The Existence of K -- 7.4 Embeddings of K and Generic Absoluteness -- 7.5 Weak Covering for K -- Notes -- 8 One Strong Cardinal -- 8.1 Premice -- 8.2 Properties of Mice -- 8.3 Extender Models up to One Strong Cardinal -- Notes -- 9 Overlapping Extenders. 9.1 Premice and Iteration Trees -- 9.2 Copying and the Dodd-Jensen Property -- 9.3 Solidity and Condensation -- 9.4 Uniqueness of Weil-Founded Branches -- 9.5 Towards the Ultimate Model Kc -- Notes -- Bibliography -- Index. Constructibility (Set theory) http://id.loc.gov/authorities/subjects/sh85031342 Large cardinals (Mathematics) http://id.loc.gov/authorities/subjects/sh94004021 Constructibilité (Théorie des ensembles) Grands cardinaux (Nombres) MATHEMATICS Set Theory. bisacsh Constructibility (Set theory) fast Large cardinals (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85031342 http://id.loc.gov/authorities/subjects/sh94004021 |
| title | Inner models and large cardinals / |
| title_auth | Inner models and large cardinals / |
| title_exact_search | Inner models and large cardinals / |
| title_full | Inner models and large cardinals / Martin Zeman. |
| title_fullStr | Inner models and large cardinals / Martin Zeman. |
| title_full_unstemmed | Inner models and large cardinals / Martin Zeman. |
| title_short | Inner models and large cardinals / |
| title_sort | inner models and large cardinals |
| topic | Constructibility (Set theory) http://id.loc.gov/authorities/subjects/sh85031342 Large cardinals (Mathematics) http://id.loc.gov/authorities/subjects/sh94004021 Constructibilité (Théorie des ensembles) Grands cardinaux (Nombres) MATHEMATICS Set Theory. bisacsh Constructibility (Set theory) fast Large cardinals (Mathematics) fast |
| topic_facet | Constructibility (Set theory) Large cardinals (Mathematics) Constructibilité (Théorie des ensembles) Grands cardinaux (Nombres) MATHEMATICS Set Theory. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=559707 |
| work_keys_str_mv | AT zemanmartin innermodelsandlargecardinals |