Israel Mathematical Conference Proceedings 1993; 654 pp; softcover Volume: 6 List Price: US$61 Member Price: US$48.80 Order Code: IMCP/6
 The branch of mathematics concerned with set theory of the reals began with Cantor's work in abstract analysis and was continued by Hausdorff, Lebesgue, Sierpinksi, Luzin, Fraenkel, Zermelo, Rothberger, Gödel, and others. Today the most important research directions are based on the work of Paul Cohen on the size of the continuum. The central problem in this area is to understand the structure of the continuum when its size is at least \(\aleph _3\). It is still generally believed that the size of the continuum should be the guiding light for further research in set theory. This book presents the proceedings of a Winter Institute on "Set Theory of the Reals" held at BarIlan University in January 1991. Containing mostly survey papers, the book provides an excellent account of present knowledge in this area and an outline for future research. Set Theory of the Reals is accessible to graduate students in set theory, abstract analysis, topology, measure theory, model theory, and logic. A publication of the BarIlan University. Distributed worldwide by the AMS. Readership Graduate students in set theory, abstract analysis, topology, measure theory, model theory, and logic, as well as researchers in these fields. Table of Contents  S. Shelah  The future of set theory
 T. Bartoszynski and H. Judah  Strong measure zero sets
 A. Blass  Simple cardinal characteristics of the continuum
 J. Brendle  Set theoretic aspects of nonabelian groups
 L. Bukovsky  Thin sets related to trigonometric series
 M. Burke  Liftings for Lebesgue measure
 D. Fremlin  Realvaluedmeasurable cardinals
 M. Goldstern  Tools for your forcing construction
 H. Judah  \(\Delta ^1_3\)sets of reals
 H. Judah and A. Rosłanowski  On Shelah's amalgamation
 A. Miller  Special sets of reals
 M. Repicky  Cardinal invariants related to porous sets
 M. Scheepers  Gaps in \(\omega ^\omega\)
 O. Spinas  Cardinal invariants and quadratic forms
 J. Steprans  Combinatorial consequences of adding Cohen reals
 P. Vojtas  Generalized GaloisTukeyconnections
 A. Miller  Arnie Miller's problem list
