On the Minimal Cofinal Subsets of a Directed Quasi Ordered Set
  
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Author NameAffiliation
Wang Shangzhi North West University 
Li Boyu North West University 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:1000-341X.1983.01.018
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