Notes on Forcing Axioms

Abstract

The Baire Category Theorem and the Baire Category Numbers Coding into the Reals Descriptive Set-Theoretic Consequences Measure-Theoretic Consequences Variations on the Souslin Hypothesis The S- and L-Space Problems 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 mm and Cardinal Arithmetic Reflection Principles Appendices: Basic Notions Preserving Stationary Sets Historical and Other Comments.