Extensions of the axiom of determinacy
Determinacy -- The wadge hierarchy -- Coding lemmas -- Properties of pointclasses -- Strong partition cardinals -- Suslin sets and uniformization -- Ordinal determinacy -- Infinity-Borel sets -- Cone measure ultraproducts -- Vopenka algebras -- Suslin sets and strong codes -- Scales from uniformizat...
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| 1. Verfasser: | |
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
2023
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| Schriftenreihe: | University lecture series
volume 78 |
| Schlagworte: |
Determinants
> Descriptive set theory
> Axiomatic set theory
> Logic, Symbolic and mathematical
> Mathematical logic and foundations -- Set theory -- Determinacy principles
> Mathematical logic and foundations -- Set theory -- Descriptive set theory
> Mathematical logic and foundations -- Set theory -- Axiom of choice and related propositions
> Mathematical logic and foundations -- Set theory -- Inner models, including constructibility, ordinal definability, and core models
> Determination
> Axiomatische Mengenlehre
> Deskriptive Mengenlehre
> Analytische Menge
> Ultraprodukt
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| Online Zugang: | zbMATH |
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Tag hinzufügen | Zusammenfassung: | Determinacy -- The wadge hierarchy -- Coding lemmas -- Properties of pointclasses -- Strong partition cardinals -- Suslin sets and uniformization -- Ordinal determinacy -- Infinity-Borel sets -- Cone measure ultraproducts -- Vopenka algebras -- Suslin sets and strong codes -- Scales from uniformization -- Real determinacy from scales. Publisher’s description: This is an expository account of work on strong forms of the Axiom of Determinacy (AD) by a group of set theorists in Southern California, in particular by W. Hugh Woodin. The first half of the book reviews necessary background material, including the Moschovakis Coding Lemma, the existence of strong partition cardinals, and the analysis of pointclasses in models of determinacy. The second half of the book introduces Woodin’s axiom system AD+ and presents his initial analysis of these axioms. These results include the consistency of AD+ from the consistency of AD, and its local character and initial motivation. Proofs are given of fundamental results by Woodin, Martin, and Becker on the relationships among AD, AD+, the Axiom of Real Determinacy, and the Suslin property. Many of these results are proved in print here for the first time. The book briefly discusses later work and fundamental questions which remain open. The study of models of AD+ is an active area of contemporary research in set theory. The presentation is aimed at readers with a background in basic set theory, including forcing and ultrapowers. Some familiarity with classical results on regularity properties for sets of reals under AD is also expected. |
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| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xiii, 165 Seiten 26 cm |
| ISBN: | 9781470472108 978-1-4704-7210-8 |