Classification and Types of Bases of All Ultrafunctions on Two-Element Set

Abstract

This paper studies properties of ultrafunctions with respect of their inclusion in maximal clones. The number of maximal clones for all ultrafunctions of rank 2 is equal to 11 [V. Panteleev, 2009]. All ultrafunctions are divided into 45 equivalence classes. Based on this classification all kinds of bases are discribed. Two bases are of different kinds if there is a function in one basis with no equivalent function in the other one. We show that bases of hyperfunctions can have cardinality from 1 to 4: there is only one kind of basis with cardinality 1, 180 with cardinality 2, 686 with cardinality 3, 28 with cardinality 4.

Keywords

• ultrafunction
• clone
• base
• maximal clone