Abstract
By H. Strietz, 1975, and G. Czedli, 1996, the complete lattice $Equ(A)$ of all equivalences is four-generated, provided the size $|A|$ is an accessible cardinal. Results of I. Chajda and G. Czedli, 1996, G. Takach, 1996, T. Dolgos, 2015, and J. Kulin 2016, show that both the lattice $Quo(A)$ of all quasiorders on $A$ and, for $|A|\leq \aleph_0$, the lattice $Tran(A)$ of all transitive relations on $A$ have small generating sets. Based on complicated earlier constructions, we derive some new results in a concise but not self-contained way.
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