GENERALIZED TOWER SPECTRA

Abstract We investigate the tower spectrum in the generalized Baire space, i.e., the set of lengths of towers in $\kappa ^\kappa $ . We show that both small and large tower spectra at all regular cardinals simultaneously are consistent. Furthermore, based on previous work by Bağ, the first author and Friedman, we prove that globally, a small tower spectrum is consistent with an arbitrarily large spectrum of maximal almost disjoint families. Finally, we show that any non-trivial upper bound on the tower spectrum in $\kappa ^\kappa $ is consistent.