Abstract

We show that there exist uncountably many pairwise nonisomorphic density-like ideals on $\omega $ which are not generalized density ideals. In addition, they are nonpathological. This answers a question posed by Borodulin-Nadzieja et al. in [this Journal, vol. 80, pp. 1268–1289]. Lastly, we provide sufficient conditions for a density-like ideal to be necessarily a generalized density ideal.