Unions of well-ordered sets
نویسندگان
چکیده
منابع مشابه
From Well-Quasi-Ordered Sets to Better-Quasi-Ordered Sets
We consider conditions which force a well-quasi-ordered poset (wqo) to be betterquasi-ordered (bqo). In particular we obtain that if a poset P is wqo and the set Sω(P ) of strictly increasing sequences of elements of P is bqo under domination, then P is bqo. As a consequence, we get the same conclusion if Sω(P ) is replaced by J (P ), the collection of non-principal ideals of P , or by AM(P ), ...
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We show that it is not possible to construct a Fraenkel-Mostowski model in which the axiom of choice for well ordered families of sets and the axiom of choice for sets for well orderable sets are both true, but the axiom of choice is false. We are concerned with the following two consequences of the axiom of choice: C(WO,∞): Every well ordered collection of sets has a choice function. C(∞,WO): ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1994
ISSN: 0263-6115
DOI: 10.1017/s1446788700034753