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Norms on Possibilities. I: Forcing with Trees and Creatures
Andrzej Rosłanowski, Boise State University, ID, and Saharon Shelah, Hebrew University of Jerusalem, Israel
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Memoirs of the American Mathematical Society
1999; 167 pp; softcover
Volume: 141
ISBN-10: 0-8218-1180-0
ISBN-13: 978-0-8218-1180-1
List Price: US$56
Individual Members: US$33.60
Institutional Members: US$44.80
Order Code: MEMO/141/671
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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 PP-property.

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
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