Geodesic
On Two Isomorphic Intervals in the Lattice of Ultraclones on Two-Elements Set
The Bulletin of Irkutsk State University. Series Mathematics, Tome 7 (2014), pp. 133-140

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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.
Keywords: clone, Boolean functions, partial functions, hyperfunctions, multifunctions.
Mots-clés : superposition 
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     author = {S. Haltanova},
     title = {On {Two} {Isomorphic} {Intervals} in the {Lattice} of {Ultraclones} on {Two-Elements} {Set}},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {133--140},
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S. Haltanova. On Two Isomorphic Intervals in the Lattice of Ultraclones on Two-Elements Set. The Bulletin of Irkutsk State University. Series Mathematics, Tome 7 (2014), pp. 133-140. http://geodesic.mathdoc.fr/item/IIGUM_2014_7_a10/