On maximal clones of ultrafunctions of rank 2
This paper considers functions mapping a 2-element set A to all nonempty subsets of A. These functions are called ultrafunctions of rank 2. Ultrafunctions of rank 2 can be interpreted as functions on all non-empty subsets of A. Value of ultrafunction on set B ⊆ A is determined as intersection of values on all elements of B, if this intersection is not empty, and as union of these values otherwise. Thus an unltrafunction can be specified by all of its values on elements of A. Superposition of ultrafunctions is determined the same way.
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