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