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

Inhalt
Talks.- Descriptive Set Theoretic Phenomena in Analysis and Topology.- An Alternative Proof of Laver's Results on the Algebra Generated by an Elementary Embedding.- Some other Problems in Set Theory.- Games in rEcursion Theory and Continuity Properties of Capping Degrees.- Admissibility and Mahloness in L(?).- Set Theory of Reals: Measure and Category.- The Structure of Borel Equivalence Relations in Polish Spaces.- Classifying bOrel Structures.- What is Mac Lane Missing?.- Is Mathias an Ontologist?.- Degrees of Constructibility.- Applications of the Open Coloring Axiom.- Research Papers.- Amoeba Forcing, Suslin Absoluteness and Additivity of Measure.- Measure and cAtegory Filters on ?.- Universally Baire Sets of Reals.- The Singular Cardinal Hypothesis Revisited.- A Weak Version of at from Oca.- One Cannot Show from ZFC that there is an Ulm Type Classification of the Countable Torsion-Free Abelian Groups.- ?1/3-Absoluteness for Sequences of Measures.- Vive la Difference i: Nonisomorphism of Ultrapowers of Countable Models.- Coding and Reshaping when there are no Sharps.