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Hyper-pseudoformulas and m-solid ordered pseudovarieties

Denecke K., Phusanga D.

Demonstratio Mathematica

2011

Vol. 44, nr 4

723-738

In 2009 K.Denecke and J.Koppitz proved that for a monoid M of hypersubstitutions M-solid positive varieties of tree languages correspond to M-solid ordered pseudovarieties. In this paper, we will characterize M-solid ordered pseudovarieties in a similar way in which in [14] M-solid varieties, in [3] M-solid quasivarieties, in [11] M-solid pseudovarieties and in [12] M-solid algebraic systems were characterized. The main idea is to show, that we have two Galois-connections and a conjugate pair of additive closure operators. Then we can apply the general theory of conjugate pairs of additive closure operators.