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This research level monograph reflects the current state of the field and provides a reference for graduate students entering the field as well as for established researchers.

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....

Designed to be the foundation for a two-term course, this book investigates mathematical logic. The basic premise of mathematical logic is that every reasonable mathematical system is intrinsically incomplete. This premise forms the basis of Godel's famous incompleteness theorem.