On the cardinal number of complete sets of Boolean operations†
作者:
E. V. KRISHNAMURTHY,
期刊:
International Journal of Control
(Taylor Available online 1970)
卷期:
Volume 11,
issue 6
页码: 1041-1046
ISSN:0020-7179
年代: 1970
DOI:10.1080/00207177008905982
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
It is shown in the literature (using the Post—Yablonsky theorem) that a complete set of Boolean operations cannot have a cardinal number greater than four. It is the object of this paper to improve this bound and prove that a complete set can have a cardinal number of at most three or, in other words, there does not exist a complete (non–redundant) set of more than three Boolean operations. The proof given here is constructive, using the Post—Yablonsky theorem, truth tables and combinatorial set theory.
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