Nearlattices

By a nearlattice is meant a join-semilattice where every principal filter is a lattice with respect to the induced order. Alternatively, a nearlattice can be described as an algebra with one ternary operation satisfying eight simple identities. Hence, the class of nearlattices is a variety. We characterize nearlattices every sublattice of which is distributive. Then we introduce the so-called section pseudocomplementation on nearlattices which can also be characterized by identities.