Abstract. By H. Strietz, 1975, and G. Czédli, 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. Czédli, 1996, G. Takách, 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.

DOI: 10.14232/actasm-016-056-2

AMS Subject Classification (1991): 06B99

Keyword(s): quasiorder lattice, lattice of preorders, minimum-sized generating set, four-generated lattice, lattice of transitive relations

Received October 4, 2016, and in revised form October 22, 2016. (Registered under 56/2016.)