In the mathematical practice, the Baire category method is a tool for establishing the existence of a rich array of generic structures. However, in mathematics, the Baire category method is also behind a number of fundamental results such as the Open Mapping Theorem or the Banach–Steinhaus Boundedness Principle. This volume brings the Baire category method to another level of sophistication via the internal version of the set-theoretic forcing technique. It is the first systematic account of applications of the higher forcing axioms with the stress on the technique of building forcing notions rather than on the relationship between different forcing axioms or their consistency strengths.
Sample Chapter(s)
Foreword (46 KB)
Chapter 1: Baire Category Theorem and the Baire Category Numbers (148 KB)
Contents:
- Baire Category Theorem and the Baire Category Numbers
- Coding Sets by the Real Numbers
- Consequences in Descriptive Set Theory
- Consequences in Measure Theory
- Variations on the Souslin Hypothesis
- The S-Spaces and the L-Spaces
- The Side-condition Method
- Ideal Dichotomies
- Coherent and Lipschitz Trees
- Applications to the S-Space Problem and the von Neumann Problem
- Biorthogonal Systems
- Structure of Compact Spaces
- Ramsey Theory on Ordinals
- Five Cofinal Types
- Five Linear Orderings
- Cardinal Arithmetic and mm
- Reflection Principles
- Appendices:
- Basic Notions
- Preserving Stationary Sets
- Historical and Other Comments
Readership: Graduate students and researchers in logic, set theory and related fields.
