This article is cited in 1 paper

Continuality of classes of functions in multivalued logic with minimal logarithmic growth rate

S. A. Komkov

Lomonosov Moscow State University

Abstract: 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.

UDC: 519.157

Received: 15.03.2021

DOI: 10.4213/dm1636

 English version: Discrete Mathematics and Applications, 2022, 32:2, 97–103

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