Canonical models for ℵ1-combinatorics Original Research Article

We define the property of Π2-compactness of a statement Φ of set theory, meaning roughly that the hard core of the impact of Φ on combinatorics of View the MathML source can be isolated in a canonical model for the statement Φ. We show that the following statements are Π2-compact: “dominating number = View the MathML source,” “cofinality of the meager ideal = View the MathML source”, “cofinality of the null ideal = View the MathML source”, “bounding number = View the MathML source”, existence of various types of Souslin trees and variations on uniformity of measure and category = View the MathML source. Several important new metamathematical patterns among classical statements of set theory are pointed out