ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2014. Vol. 7

On Two Isomorphic Intervals in the Lattice of Ultraclones on Two-Elements Set

S. Haltanova

This paper considers multifunctions on two-elements set  with superposition defined in a special way. Set of all multifunctions contains set of Boolean functions, set of partial functions and set of hyperfunctions. Clone of multifunctions is a set closed under superposition. Interval I (A, B) is a partially ordered by inclusion set of all subclones of B containing A.
This paper describes a fragment of an interval in the lattice of clones containing all multifunctions preserving 0 and 1 (if particular function simultaneously preserves 0 and 1 then it cannot have an empty set as a value on any input). It is known that interval of partial Boolean functions preserving 0 and 1 consists of 45 clones.
This paper shows that considered interval contains 12 clones and has an isomorphic interval in the lattice of clones of partial functions.

clone, superposition, Boolean functions, partial functions, hyperfunctions, multifunctions

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