良准序偏序集上的偏序集代数
Poset algebras over well quasi-ordered posets
摘要：
本文定义并研究了一类新的偏序型类$\gbqo^+$。偏序集$P$属于类$W^+ $当且仅当自由偏序集代数$F(P)$由包含在自由格$L(P)$中的更好的准序$G$生成。证明了若$P$是任一良拟序，则$L(P)$是良基的，并且是良拟序的可数并.证明了类$W^+$包含在良拟序集类中。我们证明了$W^+$在较好的拟序指标集上的同态像、有限积和字典序和下是保持的。我们还证明了每一个可数良拟序集都在$W^+$中。我们不知道，但是，如果类的良好拟序集包含在$W^+$。附加结果涉及偏序集代数的同态像。
英文摘要：
A new class of partial order-types, class $\gbqo^+$ is defined and investigated here. A poset $P$ is in the class $W^+ $ iff the free poset algebra $F(P)$ is generated by a better quasi-order $G$ that is included in the free lattice $L(P)$. We prove that if $P$ is any well quasi-ordering, then $L(P)$ is well founded, and is a countable union of well quasi-orderings. We prove that the class $W^+$ is contained in the class of well quasi-ordered sets. We prove that $W^+$ is preserved under homomorphic image, finite products, and lexicographic sum over better quasi-ordered index sets. We prove also that every countable well quasi-ordered set is in $W^+$. We do not know, however if the class of well quasi-ordered sets is contained in $W^+$. Additional results concern homomorphic images of posets algebras.
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