Abstract. Strietz [4, 5] has shown that $\mathop{\rm Equ}(A)$, the lattice of all equivalences of a finite set $A$, has a four-element generating set. We extend this result for many infinite sets $A$; even for all sets if there are no inaccessible cardinals. Namely, we prove that if $A$ is a set consisting of at least four elements and there is no inaccessible cardinal $\le |A|$, then the {\it complete} lattice $\mathop{\rm Equ}(A)$ can be generated by four elements. This result is sharp in the sense that $\mathop{\rm Equ}(A)$ cannot be generated by three elements.

AMS Subject Classification (1991): 06B99, 06C10

Keyword(s): Lattice, equivalence, equivalence lattice, generating set, inaccessible cardinal

Received September 1, 1995 and in revised form January 12, 1996. (Registered under 5708/2009.)