We prove: for every mod-finite ascending chain (indexed by an ordinal a) of infinite subsets of the set of natural numbers, there exists M, an infinite maximal almost disjoint family of infinite subsets of the natural numbers (MADF), such that the Stone-Cˇech remainder of the psi-space associated with M is homeomorphic to a + 1 with the order topology. We also prove that for every ordinal a less than the successor cardinal to the tower number, there exists a mod-finite ascending chain indexed by a, hence a psi-space with Stone-Cech remainder homeomorphic to a + 1. This generalizes a result credited to S. Mrowka by J. Terasawa which states that there is MADF M such that Stone-Cech remainder of the psi-space associated with M is homeomorphic the first uncountable successor ordinal.