English

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 SCCcof\text{SCC}^{\text{cof}}, and proved that it is equivalent to several statements, including the assertion that Namba forcing is semiproper. We introduce an apparently weaker version, denoted SCCsplit\text{SCC}^{\text{split}}, and prove an analogous characterization of it. In particular, SCCsplit\text{SCC}^{\text{split}} 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}
}