We study autocorrelation inequalities, in the spirit of Barnard and Steinerberger's work [1]. In particular, we obtain improvements on sharp constants some inequalities previously considered by these authors, also prove existence extremizers to certain specific settings. Our methods consist relating question other classical Four...

Abstract The main purpose of this dissertation is to apply and develop new forcing techniques obtain models where several cardinal characteristics are pairwise different as well force many (even more, continuum many) values that parametrized by reals. In particular, we look at associated with strong measure zero, Yorioka ideals, localization anti-localization cardinals. thesis introduce the pro...