The paper 3] was devoted to an extensive study of the interval of the lattice of semigroup pseudovarieties between the pseudovarieties O and PO generated by all semigroups of full and respectively, partial, order preserving transformations of a nite chain. It was shown that not only the interval O; PO] itself but also many of its naturally arising subintervals are huge in the sense that they all contain a chain isomorphic to the chain of reals with the usual order as well as an antichain of the

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... cardinality of the continuum. However, at least one important question concerning the relative location of the pseudovarieties O and PO was left open in 3]. To formulate the question, let us rst recall two observations rst made in 4]: the pseudovariety O is self-dual, that is, for each semigroup S 2 O, the dual semigroup S belongs to O as well 4, Theorem 2.4]; the pseudovariety PO is not self-dual, more precisely, there exists a nite R-trivial semigroup S 2 PO such that the dual semigroup S is not in PO 4, Result 4.1]. Denoting by PO the dual of the pseudovariety PO, we see that the selfduality of O and the inclusion O PO imply the \dual" inclusion O PO . Therefore we also have the inclusion O PO \ PO :