Complete ordered sets with no infinite antichains

نویسندگان

Dwight Duffus

Maurice Pouzet

Ivan Rival

چکیده

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 familiar “completion by cuts” or normal compktion N(P) which con&s of all subsets S of P satisfying (S), = S, where, for X s P we define

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