Ebook: Set Theory of the Continuum

Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include: J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S. Kechris, A. Louveau, S. MacLane, M. Magidor, A.R.D. Mathias, G. Melles, W.J. Mitchell, S. Shelah, R.A. Shore, R.I. Soare, L.J. Stanley, B. Velikovic, H. Woodin

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Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include: J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S. Kechris, A. Louveau, S. MacLane, M. Magidor, A.R.D. Mathias, G. Melles, W.J. Mitchell, S. Shelah, R.A. Shore, R.I. Soare, L.J. Stanley, B. Velikovic, H. Woodin
Content:
Front Matter....Pages i-ix
Descriptive Set Theoretic Phenomena in Analysis and Topology....Pages 1-25
An Alternative Proof of Laver’s Results on the Algebra Generated by an Elementary Embedding....Pages 27-33
Some other Problems in Set Theory....Pages 35-38
Games in Recursion Theory and Continuity Properties of Capping Degrees....Pages 39-62
Admissibility and Mahloness in L(?)....Pages 63-74
Set Theory of Reals: Measure and Category....Pages 75-87
The Structure of Borel Equivalence Relations in Polish Spaces....Pages 89-102
Classifying Borel Structures....Pages 103-112
What is Mac Lane Missing?....Pages 113-118
Is Mathias an Ontologist?....Pages 119-122
Degrees of Constructibility....Pages 123-135
Applications of the Open Coloring Axiom....Pages 137-154
Amoeba Forcing, Suslin Absoluteness and Additivity of Measure....Pages 155-173
Measure and Category — Filters on ?....Pages 175-201
Universally Baire Sets of Reals....Pages 203-242
The Singular Cardinal Hypothesis Revisited....Pages 243-279
A Weak Version of at from OCA....Pages 281-291
One Cannot Show from ZFC that there is an Ulm-Type Classification of the Countable Torsion-Free Abelian Groups....Pages 293-309
Vive la Diff?rence I: Nonisomorphism of Ultrapowers of Countable Models....Pages 311-355
Coding and Reshaping when there are no Sharps....Pages 357-405
Erratum to: Vive la Diff?rence I: Nonisomorphism of Ultrapowers of Countable Models....Pages 407-416
Back Matter....Pages 419-419
....Pages 417-417