Minimal partial hyperclones on a two-element set

Abstract

Let A be a two-element set. It has been proven by Machida that the lattice of hyperclones has continuum cardinality. The current paper first determines all the minimal partial hyperclones. Following this, the authors give all three-element subsets of minimal hyperoperations whose union generates the clone of all hyperoperations as well as all four minimal subsets of minimal partial hyperoperations whose union generates the clone of all partial hyperoperations.