# Large Cardinals, Determinacy and Other TopicsThe Cabal Seminar, Volume IV

Volume 4

## $130.00 (C) Part of Lecture Notes in Logic Paul B. Larson, Alexander S. Kechris, Robert M. Solovay, Donald A. Martin, W. Hugh Woodin, Ilijas Farah, John R. Steel, Claude Dellacherie, Matthew Foreman, Andrés Eduardo Caicedo, Benedikt Löwe View all contributors • Date Published: November 2020 • availability: Available • format: Hardback • isbn: 9781107182998 ##$130.00 (C) Hardback

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• 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final volume in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes.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.

• Includes updated/revised material from the original Cabal Seminars volume
• New, unpublished survey articles put the historical papers into context
• Now includes uniform and modern notation to make the book more accessible to the reader

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## Product details

• Date Published: November 2020
• format: Hardback
• isbn: 9781107182998
• length: 270 pages
• dimensions: 160 x 235 x 25 mm
• weight: 0.63kg
• contains: 2 tables
• availability: Available

Preface
Original numbering
Part VII. Extensions of AD, models with choice:
1. A brief history of determinacy Paul B. Larson
2. “AD plus uniformization” is equivalent to “half $AD_\mathbb{R}$” Alexander S. Kechris
3. The independence of DC from AD Robert M. Solovay
4. Games of countable length Donald A. Martin
5. Some consistency results in ZFC using AD W. Hugh Woodin
6. Subsets of $\aleph_1$ constructible from a real Alexander S. Kechris
7. AD and the uniqueness of the supercompact measures on $\wp_{\omega_1}(\lambda)$ W. Hugh Woodin
8. The extender algebra and $\sum_1^2$-absoluteness Ilijas Farah
Part VIII. Other topics:
9. On Vaught's conjecture John R. Steel
10. Capacities and analytic sets Claude Dellacherie
11. More saturated ideals Matthew Foreman
12. The fourteen Victoria Delfino problems and their status in the year 2020 Andrés Eduardo Caicedo and Benedikt Löwe
Bibliography.

• ## Editors

Alexander S. Kechris, California Institute of Technology
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, Universiteit van Amsterdam
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, University of California, Berkeley
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.

## Contributors

Paul B. Larson, Alexander S. Kechris, Robert M. Solovay, Donald A. Martin, W. Hugh Woodin, Ilijas Farah, John R. Steel, Claude Dellacherie, Matthew Foreman, Andrés Eduardo Caicedo, Benedikt Löwe

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