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

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In [3], a basis of identities {un ≈ vn | n ≥ 2} for the variety SPS of all strict pseudosemilattices was determined. Each one of these identities un ≈ vn has a peculiar 2-content Dn. In this paper we study the varieties of pseudosemilattices defined by sets of identities, all with 2-content the same Dn. We present here the family of all these varieties and show that each variety from this family is defined by a single identity also with 2-content Dn. This paper ends with the study of the inclusion relation between the varieties of this family.