Memoirs of the American Mathematical Society 1999; 167 pp; softcover Volume: 141 ISBN10: 0821811800 ISBN13: 9780821811801 List Price: US$59 Individual Members: US$35.40 Institutional Members: US$47.20 Order Code: MEMO/141/671
 Abstract. In this Memoir we present a systematic study of the method of norms on possibilities of building forcing notions with keeping their properties under full control. This technique allows us to answer several open problems, but on our way to get the solutions we develop various ideas interesting per se. These include a new iterable condition for "not adding Cohen reals" (which has a flavour of preserving special properties of \(p\)points), new intriguing properties of ultrafilters (weaker than being Ramsey but stronger than \(p\)point) and some new applications of variants of the PPproperty. Readership Graduate students and research mathematicians interested in mathematical logic and foundations. Table of Contents  Introduction
 Basic definitions
 Preperness and the reading of names
 More properties
 Omittory with Halving
 Around not adding Cohen reals
 Playing with ultrafilters
 Friends and relatives of PP
 List of definitions
 Bibliography
