Memoirs of the American Mathematical Society 2004; 141 pp; softcover Volume: 167 ISBN10: 0821834509 ISBN13: 9780821834503 List Price: US$64 Individual Members: US$38.40 Institutional Members: US$51.20 Order Code: MEMO/167/793
 The subject of the book is the relationship between definable forcing and descriptive set theory. The forcing serves as a tool for proving independence of inequalities between cardinal invariants of the continuum. The analysis of the forcing from the descriptive point of view makes it possible to prove absoluteness theorems of the type "certain forcings are the provably best attempts to achieve consistency results of certain syntactical form" and others. There are connections to such fields as pcf theory, effective descriptive set theory, determinacy and large cardinals, Borel equivalence relations, abstract analysis, and others. Readership Graduate students and research mathematicians interested in mathematical logic and foundations. Table of Contents  Introduction
 Definable forcing adding a single real
 The countable support iterations
 Other forcings
 Applications
 Examples of cardinal invariants
 The syntax of cardinal invariants
 Effective descriptive set theory
 Large cardinals
