Well Quasi-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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A new class of partial order-types, class G bqo is defined and investigated here. A poset P is in the class G bqo iff the poset algebra F (P ) is generated by a better quasi-order G that is included in L(P ). The free Boolean algebra F (P ) and its free distrivutive lattice L(P ) were defined in [ABKR]. The free Boolean algebra F (P ) contains the partial order P and is generated by it: F (P ) ...
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It is known that the \pattern containment" order on permutations is not a partial well-order. Nevertheless, many naturally de ned subsets of permutations are partially well-ordered, in which case they have a strong nite basis property. Several classes are proved to be partially well-ordered under pattern containment. Conversely, a number of new antichains are exhibited that give some insight as...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1993
ISSN: 0001-8708
DOI: 10.1006/aima.1993.1004