Geodesic
Continuality of classes of functions in multivalued logic with minimal logarithmic growth rate
Diskretnaya Matematika, Tome 33 (2021) no. 3, pp. 54-63

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We show that in multivalued logic there exist a continual family of pairwise incomparable closed sets with minimal logarithmic growth rate and a continual chain of nested closed sets with minimal logarithmic growth rate. As a corollary we prove that any subset-preserving class in multivalued logic contains a continual chain of nested closed sets and a continual family of pairwise incomparable closed sets such that none of the sets is a subset of any other precomplete class.
Keywords: growth rate, generating sets, finite sets, lattice of clones. 
@article{DM_2021_33_3_a3,
     author = {S. A. Komkov},
     title = {Continuality of classes of functions in multivalued logic with minimal logarithmic growth rate},
     journal = {Diskretnaya Matematika},
     pages = {54--63},
     publisher = {mathdoc},
     volume = {33},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_3_a3/}
}
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S. A. Komkov. Continuality of classes of functions in multivalued logic with minimal logarithmic growth rate. Diskretnaya Matematika, Tome 33 (2021) no. 3, pp. 54-63. http://geodesic.mathdoc.fr/item/DM_2021_33_3_a3/