Simple theories and hyperimaginaries /:
"This book is a self-contained, up-to-date introduction to simple theories and the model theory of hyperimaginaries"--Provided by publisher.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Cambridge University Press,
2011.
|
| Schriftenreihe: | Lecture notes in logic ;
39. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "This book is a self-contained, up-to-date introduction to simple theories and the model theory of hyperimaginaries"--Provided by publisher. "In the 1990s Byunghan Kim and Anand Pillay generalized stability, a major model-theoretic idea developed by Saharon Shelah twenty-five years earlier, to the study of simple theories. This book is an up-to-date introduction to simple theories and hyperimaginaries, with special attention to Lascar strong types and elimination of hyperimaginary problems. Assuming only knowledge of general model theory, the foundations of forking, stability, and simplicity are presented in full detail. The treatment of the topics is as general as possible, working with stable formulas and types and assuming stability of the theory only when necessary. The author offers an introduction to independence relations as well as a full account of canonical bases of types in stable and simple theories. In the last chapters, the notions of internality and analyzability are discussed and used to provide a self-contained proof of elimination of hyperimaginaries in supersimple theories"--Provided by publisher. |
| Beschreibung: | 1 online resource (xiv, 169 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781139003728 1139003720 9781139092913 113909291X |
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| author | Casanovas, Enrique, 1957- |
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| contents | Preliminaries -- x, y-Types, stability and simplicity -- x, y-Types and the local rank D -- Forking -- Independence -- The local rank CB x, y (pi) -- Heirs and coheirs -- Stable forking -- Lascar strong types -- The independence theorem -- Canonical bases -- Abstract independence relations -- Supersimple theories -- More ranks -- Hyperimaginaries -- Hyperimaginary forking -- Canonical bases revisited -- Elimination of hyperimaginaries -- Orthogonality and analysability -- Hyperimaginaries in supersimple theories. |
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| indexdate | 2024-11-27T13:18:21Z |
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| series2 | Lecture notes in logic ; |
| spelling | Casanovas, Enrique, 1957- https://id.oclc.org/worldcat/entity/E39PBJy4dpKVXpk7VHV98DHQv3 http://id.loc.gov/authorities/names/n2011008486 Simple theories and hyperimaginaries / Enrique Casanovas. New York : Cambridge University Press, 2011. 1 online resource (xiv, 169 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Lecture notes in logic ; 39 Includes bibliographical references and index. Preliminaries -- x, y-Types, stability and simplicity -- x, y-Types and the local rank D -- Forking -- Independence -- The local rank CB x, y (pi) -- Heirs and coheirs -- Stable forking -- Lascar strong types -- The independence theorem -- Canonical bases -- Abstract independence relations -- Supersimple theories -- More ranks -- Hyperimaginaries -- Hyperimaginary forking -- Canonical bases revisited -- Elimination of hyperimaginaries -- Orthogonality and analysability -- Hyperimaginaries in supersimple theories. "This book is a self-contained, up-to-date introduction to simple theories and the model theory of hyperimaginaries"--Provided by publisher. "In the 1990s Byunghan Kim and Anand Pillay generalized stability, a major model-theoretic idea developed by Saharon Shelah twenty-five years earlier, to the study of simple theories. This book is an up-to-date introduction to simple theories and hyperimaginaries, with special attention to Lascar strong types and elimination of hyperimaginary problems. Assuming only knowledge of general model theory, the foundations of forking, stability, and simplicity are presented in full detail. The treatment of the topics is as general as possible, working with stable formulas and types and assuming stability of the theory only when necessary. The author offers an introduction to independence relations as well as a full account of canonical bases of types in stable and simple theories. In the last chapters, the notions of internality and analyzability are discussed and used to provide a self-contained proof of elimination of hyperimaginaries in supersimple theories"--Provided by publisher. Model theory. http://id.loc.gov/authorities/subjects/sh85086421 First-order logic. http://id.loc.gov/authorities/subjects/sh85048595 Hyperspace. http://id.loc.gov/authorities/subjects/sh85063720 Théorie des modèles. Logique du premier ordre. Hyperespace. MATHEMATICS Logic. bisacsh MATHEMATICS General. bisacsh Modelos matemáticos embne First-order logic fast Hyperspace fast Model theory fast has work: Simple theories and hyperimaginaries (Text) https://id.oclc.org/worldcat/entity/E39PCGwHMc9MQDJrBKG8Mx9TRC https://id.oclc.org/worldcat/ontology/hasWork Print version: Casanovas, Enrique, 1957- Simple theories and hyperimaginaries. New York : Cambridge University Press, 2011 (DLC) 2011005729 Lecture notes in logic ; 39. http://id.loc.gov/authorities/names/n93082404 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=369480 Volltext |
| spellingShingle | Casanovas, Enrique, 1957- Simple theories and hyperimaginaries / Lecture notes in logic ; Preliminaries -- x, y-Types, stability and simplicity -- x, y-Types and the local rank D -- Forking -- Independence -- The local rank CB x, y (pi) -- Heirs and coheirs -- Stable forking -- Lascar strong types -- The independence theorem -- Canonical bases -- Abstract independence relations -- Supersimple theories -- More ranks -- Hyperimaginaries -- Hyperimaginary forking -- Canonical bases revisited -- Elimination of hyperimaginaries -- Orthogonality and analysability -- Hyperimaginaries in supersimple theories. Model theory. http://id.loc.gov/authorities/subjects/sh85086421 First-order logic. http://id.loc.gov/authorities/subjects/sh85048595 Hyperspace. http://id.loc.gov/authorities/subjects/sh85063720 Théorie des modèles. Logique du premier ordre. Hyperespace. MATHEMATICS Logic. bisacsh MATHEMATICS General. bisacsh Modelos matemáticos embne First-order logic fast Hyperspace fast Model theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85086421 http://id.loc.gov/authorities/subjects/sh85048595 http://id.loc.gov/authorities/subjects/sh85063720 |
| title | Simple theories and hyperimaginaries / |
| title_auth | Simple theories and hyperimaginaries / |
| title_exact_search | Simple theories and hyperimaginaries / |
| title_full | Simple theories and hyperimaginaries / Enrique Casanovas. |
| title_fullStr | Simple theories and hyperimaginaries / Enrique Casanovas. |
| title_full_unstemmed | Simple theories and hyperimaginaries / Enrique Casanovas. |
| title_short | Simple theories and hyperimaginaries / |
| title_sort | simple theories and hyperimaginaries |
| topic | Model theory. http://id.loc.gov/authorities/subjects/sh85086421 First-order logic. http://id.loc.gov/authorities/subjects/sh85048595 Hyperspace. http://id.loc.gov/authorities/subjects/sh85063720 Théorie des modèles. Logique du premier ordre. Hyperespace. MATHEMATICS Logic. bisacsh MATHEMATICS General. bisacsh Modelos matemáticos embne First-order logic fast Hyperspace fast Model theory fast |
| topic_facet | Model theory. First-order logic. Hyperspace. Théorie des modèles. Logique du premier ordre. Hyperespace. MATHEMATICS Logic. MATHEMATICS General. Modelos matemáticos First-order logic Hyperspace Model theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=369480 |
| work_keys_str_mv | AT casanovasenrique simpletheoriesandhyperimaginaries |