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Set Theory of the Reals
Edited by: Haim Judah
A publication of Bar-Ilan University.
Israel Mathematical Conference Proceedings
1993; 654 pp; softcover
Volume: 6
List Price: US$61
Member Price: US$48.80
Order Code: IMCP/6
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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 Bar-Ilan 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 Bar-Ilan 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 non-abelian groups
  • L. Bukovsky -- Thin sets related to trigonometric series
  • M. Burke -- Liftings for Lebesgue measure
  • D. Fremlin -- Real-valued-measurable 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 Galois-Tukey-connections
  • A. Miller -- Arnie Miller's problem list
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