Some basic thoughts on the cofiality of Chang structures with an application to forcing

Dominik Adolf

Consider $({\kappa }^{+++},{\kappa }^{++})\twoheadrightarrow ({\kappa }^{+},\kappa )$ where $\kappa$ is an uncountable regular cardinal. By a result of Shelah's we have $\mathrm{cof}(X\cap {\kappa }^{++})=\kappa$ for alm…