Canonical models for aleph_1 combinatorics
逻辑
2009-09-25 v1
摘要
We define the property of Pi_2-compactness of a statement phi of set theory, meaning roughly that the hard core of the impact of phi on combinatorics of aleph_1 can be isolated in a canonical model for the statement phi. We show that the following statements are Pi_2-compact: ``dominating number = aleph_1,'' ``cofinality of the meager ideal = aleph_1'', ``cofinality of the null ideal = aleph_1'', existence of various types of Souslin trees and variations on uniformity of measure and category = aleph_1. Several important new metamathematical patterns among classical statements of set theory are pointed out.
关键词
引用
@article{arxiv.math/9806166,
title = {Canonical models for aleph_1 combinatorics},
author = {Saharon Shelah and Jindřich Zapletal},
journal= {arXiv preprint arXiv:math/9806166},
year = {2009}
}