A variant of Shelah's characterization of Strong Chang's Conjecture
Logic
2018-11-16 v1
Abstract
Shelah considered a certain version of Strong Chang's Conjecture, which we denote , and proved that it is equivalent to several statements, including the assertion that Namba forcing is semiproper. We introduce an apparently weaker version, denoted , and prove an analogous characterization of it. In particular, is equivalent to the assertion that the the Friedman-Krueger poset is semiproper. This strengthens and sharpens the results of Cox, and sheds some light on problems from Usuba and Torres-Perez and Wu.
Keywords
Cite
@article{arxiv.1811.06402,
title = {A variant of Shelah's characterization of Strong Chang's Conjecture},
author = {Sean Cox and Hiroshi Sakai},
journal= {arXiv preprint arXiv:1811.06402},
year = {2018}
}