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In this paper the notion of weak chain-completeness is introduced for pseudo-ordered sets as an extension of the notion of chain-completeness of posets (see [3]) and it is shown that every isotone map of a weakly chain-complete pseudo-ordered set into itself has a least fixed point.
Let be a unital -ring. For any we define the weighted -core inverse and the weighted dual -core inverse, extending the -core inverse and the dual -core inverse, respectively. An element has a weighted -core inverse with the weight if there exists some such that , and . Dually, an element has a weighted dual -core inverse with the weight if there exists some such that , and . Several characterizations of weighted -core invertible and weighted dual -core invertible...
We show that, assuming PFA, the class of all Aronszajn lines is well-quasi-ordered by embeddability.
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