Canonical models for aleph1 combinatorics
Abstract
We define the property of Pi2-compactness of a statement phi of set theory, meaning roughly that the hard core of the impact of phi on combinatorics of aleph1 can be isolated in a canonical model for the statement phi. We show that the following statements are Pi2-compact: ``dominating number = aleph1,'' ``cofinality of the meager ideal = aleph1'', ``cofinality of the null ideal = aleph1'', existence of various types of Souslin trees and variations on uniformity of measure and category = aleph1. Several important new metamathematical patterns among classical statements of set theory are pointed out.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.