Contemporary Mathematics 1989; 116 pp; softcover Volume: 84 Reprint/Revision History: reprinted 1991 ISBN10: 0821850911 ISBN13: 9780821850916 List Price: US$36 Member Price: US$28.80 Order Code: CONM/84
 This book presents results on the case of the Ramsey problem for the uncountable: When does a partition of a square of an uncountable set have an uncountable homogeneous set? This problem most frequently appears in areas of general topology, measure theory, and functional analysis. Building on his solution of one of the two most basic partition problems in general topology, the "Sspace problem," the author has unified most of the existing results on the subject and made many improvements and simplifications. The first eight sections of the book require basic knowldege of naive set theory at the level of a first year graduate or advanced undergraduate student. The book may also be of interest to the exclusively settheoretic reader, for it provides an excellent introduction to the subject of forcing axioms of set theory, such as Martin's axiom and the Proper forcing axiom. Table of Contents  The role of countability in (S) and (L)
 Oscillating real numbers
 The conjecture (S) for compact spaces
 Some problems closely related to (S) and (L)
 Diagonalizations of length continuum
 (S) and (L) and the Souslin hypothesis
 (S) and (L) and Luzin spaces
 Forcing axioms for \(ccc\) partitions
 Proper forcing axioms and partitions
 (S) and (L) are different
