A new model, in terms of finite bipartite graphs, of the free
pseudosemilattice is presented. This will then be used to obtain several
results about the variety SPS of all strict pseudosemilattices: (i) an identity
basis for SPS is found, (ii) SPS is shown to be inherently non-finitely based,
(iii) SPS is shown to have no irredundant identity basis, and (iv) SPS is shown
to have no covers and to be meet-prime in the lattice of all varieties of
pseudosemilattices. Some applications to e-varieties of locally inverse
semigroups are also derived.Comment: 31 pages. In this version a few typos have been correcte
