Geodesic
Classification and types of bases of all ultrafunctions on two-element set
The Bulletin of Irkutsk State University. Series Mathematics, Tome 16 (2016), pp. 58-70

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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
Mots-clés : maximal clone. 
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     author = {S. V. Zamaratskaya and V. I. Panteleev},
     title = {Classification and types of bases of all ultrafunctions on two-element set},
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     url = {http://geodesic.mathdoc.fr/item/IIGUM_2016_16_a4/}
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S. V. Zamaratskaya; V. I. Panteleev. Classification and types of bases of all ultrafunctions on two-element set. The Bulletin of Irkutsk State University. Series Mathematics, Tome 16 (2016), pp. 58-70. http://geodesic.mathdoc.fr/item/IIGUM_2016_16_a4/