Next: Alioune Ngom - Set-valued Up: Orders, Lattices and Universal Previous: Hans-Karl Keiser - To
Hajime Machida - Hyperclones on the two-element setzo
| HAJIME MACHIDA, Hitsotsubasji University, Kunitachi, Tokyo 186-8601, Japan |
| Hyperclones on the two-element setzo |
Recently, I. G. Rosenberg initiated the study of hyperoperations and
hyperclones. For a set A, a hyperoperation on A is a mapping from
to the set of non-empty subsets of A and a
hyperclone on A is a composition-closed set of hyperoperations. Here
we study some basic properties of hyperoperations and hyperclones. In
particular, we show that the lattice of hyperclones on the two-element
set 
has the cardinality of continuum. This answers
affirmatively to Rosenberg's problem posed in 1998.
