On the structure of maximal closed sets of Pk2

The set functions of a clone of P_k2 (mapping the set {0, 1, . . ., k-1}ⁿ into {0,1}, n=1, 2, . . .) is divided into equivalence classes so that two functions are in the same class if their membership in the maximal subclones of the clone coincides. This also leads to a natural classification of the set of bases (i.e. irredundant complete subsets) of the clone. The authors determine all nonempty classes of functions of all maximal clones of P_k2:T´₀, T´₁, S´, L´ and Z_it (0⩽t<i⩽k-1, 2⩽i) except M´. Also given is the maximal number of elements in a base for each of these sets (for S´ it is proved that its upper bound is 2k). Numerical values on the number of bases are given for 2⩽k⩽10