Maximal Hyperclones on E2 as Hypercores
Hajime Machida and Jovanka Pantović
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. A hyperclone C1 is a hypercore of a clone C if its extension C#1 is contained in C and C1 is not contained in any other hyperclone having the same property. We describe six maximal hyperclones on the two-elements set as hypercores of particular clones on three element set. The interval of hyperclones on {0, 1} between the clone of all projections and the one generated by all unary hyperoperations is also completely determined.
Keywords: Hyperclone, maximal hyperclone.