Complete ordered sets with no infinite antichains
نویسندگان
چکیده
منابع مشابه
Complete ordered sets with no infinite antichains
There are several standard constructions by which an arbitrary ordered set P is extended to one in which every subset has an. infimum and a supremuma complete ordered set. The collection I(P) of all initial segments of P ordered by inclusion is one. [A subset I of P is an initial segment if, for x, y E P, x E I whenever x s y and y E I.] I(P) is a complete distributive lattice. AnoWr is the fam...
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One approach to analyzing the structure of an ordered set has been to characterize its structure in terms of that of related objects, and vice versa. For example results in [2] characterize in terms of the ordered set P when the lattice Z(P) of lower sets (also called initial segments) of P and the ordered set Id(P) of order ideals (or simply ideals) of P have infinite antichains. The results i...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1981
ISSN: 0012-365X
DOI: 10.1016/0012-365x(81)90200-4