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

  • Stepan A. Komkov EMAIL logo
Published/Copyright: April 13, 2022

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.


Note: Originally published in Diskretnaya Matematika (2021) 33,№3, 54–63 (in Russian).


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Received: 2021-03-15
Published Online: 2022-04-13
Published in Print: 2022-04-26

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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