Lattice generation of small equivalences of a countable set (Q1815846)

The author describes a generalization of Strietz and Zádori's results about four-element generating sets of the lattice \(\text{Equ} (A)\) of equivalences for a finite set \(A\). Main result: Let \(A\) be a countable set. Then there is a four-generated sublattice \(Q\) of \(\text{Equ} (A)\) such that \(Q\) contains all the atoms of \(\text{Equ} (A)\). Moreover, \(Q\) can be generated by a four-element subset of type \(1+1+2\), and also by a four-element antichain. The present paper simplifies essentially the proof for the countable case.