This article is cited in 1 paper

Classification and types of bases of all ultrafunctions on two-element set

S. V. Zamaratskaya^a, V. I. Panteleev<sup>b

a</sup> Medical Information-Analytic Center of Irkutsk Region, 2, Kalandarishvili, Irkutsk, 664011
^b Irkutsk State University, 1, K. Marx st., Irkutsk, 664003

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.

UDC: 519.7

MSC: 08A99,03B50