王尚志,李伯渝.拟序定向集最小共尾部分的结构[J].数学研究及应用,1983,3(1):91~92
拟序定向集最小共尾部分的结构
On the Minimal Cofinal Subsets of a Directed Quasi Ordered Set
  
DOI:10.3770/j.issn:1000-341X.1983.01.018
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王尚志 西北大学 
李伯渝 西北大学 
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      It is shown that for any directed quasi ordered set (Q,≤),there is a minimal ordinal number λ such that every cofinal subset of Q contains a cofinal subset which is the o-th class original set of a λ-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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