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 δ-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. © 2008 IEEE.