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On the minimal cofinal subsets of a directed quasi-ordered set

✍ Scribed by Wang Shang-Zhi; Li Bo-Yu

Publisher: Elsevier Science
Year: 1984
Tongue: English
Weight: 818 KB
Volume: 48
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90189-4

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✦ Synopsis

It is shown that for any directed quasi-ordered set (Q, ~<), there is a minimal ordinal number h such that every cofinal subset of Q contains a cofinal subset which is the 0-th class original set of a pure h-th class chain of Q. A special case of our results gives necessary and sufficient conditions for a directed set to contain a cofinal chain.

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