Norms on possibilities. I. Forcing with trees and creatures
About this Title
Andrzej Rosłanowski and Saharon Shelah
Publication: Memoirs of the American Mathematical Society
Publication Year
1999: Volume 141, Number 671
ISBNs: 978-0-8218-1180-1 (print); 978-1-4704-0262-4 (online)
DOI: http://dx.doi.org/10.1090/memo/0671
MathSciNet review: 1613600
MSC: Primary 03E05; Secondary 03E35, 03E40, 03E55
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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
Chapters
- 0. Introduction
- 1. Basic definitions
- 2. Properness and the reading of names
- 3. More properties
- 4. Omittory with Halving
- 5. Around not adding Cohen reals
- 6. Playing with ultrafilters
- 7. Friends and relatives of PP
