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

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2022-04-01 DOI:10.1515/dma-2022-0009

Stepan Alekseevich Komkov

引用次数: 0

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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具有最小对数增长率的多值逻辑中函数类的连续性

摘要我们证明了在多值逻辑中存在具有最小对数增长率的成对不可比闭集的连续族和具有最小对数生长率的嵌套闭集的持续链。作为推论，我们证明了多值逻辑中任何保留子集的类都包含嵌套闭集的连续链和成对不可比闭集的持续族，使得这些集都不是任何其他预完备类的子集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.