Abstract
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.
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