ABSTRACT
For any set A , the set Oa of all operations defined on A is closed under com position of operations and contains the projection operations. Such a set of operations is called a clone of operations on A. The collection of all clones on a given set A forms a lattice, the subclone lattice C(Oa) of Oa-When A is the special set {0,1}, the operations on A are called Boolean functions, and the subclones in C(Oa) are called Boolean clones. The lattice of all Boolean clones is countably infinite, and a complete description of it was first given by Post in 1921 in [164]. For sets A of cardinality greater than two, the lattices C(Oa) are uncountably infinite, and their structure is largely unknown. We do however have a complete description of the maximal subclones on any finite set A 1 due to Rosenberg ([178], [180]).
