Large Cardinals, Determinacy and Other Topics is the last in a series of four books presenting the seminal papers from the Caltech-UCLA 'Cabal Seminar' with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes.
The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Large Cardinals, Determinacy and Other Topics is the final volume in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. This final volume contains Parts VII and VIII of the series. Part VII focuses on 'Extensions of AD, models with choice', while Part VIII ('Other topics') collects material important to the Cabal that does not fit neatly into one of its main themes. These four volumes will be a necessary part of the book collection of every set theorist.
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The final volume in a series of four books presenting the seminal papers from the Caltech-UCLA 'Cabal Seminar'.
| Preface |
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vii | |
| Original Numbering |
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xi | |
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PART VII EXTENSIONS OF AD. MODELS WITH CHOICE |
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A brief history of determinacy |
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3 | (58) |
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"AD plus Uniformization" is equivalent to "Half ADR" |
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61 | (5) |
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The independence of DC from AD |
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66 | (30) |
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Games of countable length |
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96 | (8) |
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Some consistency results in ZFC using AD |
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104 | (26) |
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Subsets of N1 constructible from a real |
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130 | (6) |
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AD and the uniqueness of the supercompact measures on δω (λ) |
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136 | (5) |
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The extender algebra and Σ12-absoluteness |
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141 | (38) |
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179 | (17) |
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Capacities and analytic sets |
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196 | (27) |
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223 | (25) |
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The fourteen Victoria Delfino problems and their status in the year 2020 |
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248 | (33) |
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| Bibliography |
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281 | |
Alexander S. Kechris is Professor of Mathematics at the California Institute of Technology. He is the recipient of numerous honors, including the J. S. Guggenheim Memorial Foundation Fellowship and the Carol Karp Prize of the Association for Symbolic Logic. He is also a member of the Scientific Research Board of the American Institute of Mathematics. Benedikt Löwe is Universitair Hoofddocent at the Universiteit van Amsterdam, Professor of Mathematics at the Universität Hamburg and Fellow of Churchill College at the University of Cambridge. He is currently the president of the Deutsche Vereinigung für Mathematische Logik und für Grundlagenforschung der Exakten Wissenschaften (DVMLG) and the Secretary General of the Division for Logic, Methodology and Philosophy of Science and Technology (DLMPST). John R. Steel is Professor of Mathematics at the University of California, Berkeley. Prior to that, he was a professor in the mathematics department at the University of California, Los Angeles. He is a recipient of the Carol Karp Prize of the Association for Symbolic Logic and of a Humboldt Prize. Steel is also a former Fellow at the Wissenschaftskolleg zu Berlin and the Sloan Foundation.
