| 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 results by Cox and sheds some light on problems posed by Usuba, Torres‐Perez and Wu. |
