On Maximal Hyperclones on {0, 1} A New Approach

Abstract

The set of clones of operations on {0,1} forms a countable lattice which was classified by Post. The cardinality of the lattice of hyperclones on {0,1} was proved by Machida to be of the continuum. The hypercore of a clone C is zeta- closure of the set of hyperoperations whose extended operations belong to C. For every clone C which is intersection of the clone B5 and another submaximal clone of B2, we investigate hypercores. The interval of hyperclones on {0,1} generated by unary hyperoperations is also completely determined.